Which one of the following expressions does not define a geometric sequence?
| A. |
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| B. |
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| C. |
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| D. |
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| E. |
PATTERNS, FUR1 2015 VCAA 7 MC
A plant was 80 cm tall when planted in a garden.
After it was planted in the garden, its height increased by 16 cm in the first year.
It grew another 12 cm in the second year and another 9 cm in the third year.
Assuming that this pattern of geometric growth continues, the plant will grow to a maximum height of
A.
B.
C.
D.
E.
PATTERNS, FUR1 2015 VCAA 5 MC
A family bought a country property.
At the end of the first year, there were two thistles per hectare on the property.
At the end of the second year, there were six thistles per hectare on the property.
At the end of the third year, there were 18 thistles per hectare on the property.
Assume the number of thistles per hectare continues to follow a geometric pattern of growth.
At the end of the seventh year, the number of thistles per hectare is expected to be
A.
B.
C.
D.
E.
PATTERNS, FUR1 2015 VCAA 4 MC
The amount added to a new savings account each month follows a geometric sequence.
In the first month, $64 was added to the account.
In the second month, $80 was added to the account.
In the third month, $100 was added to the account.
Assuming this sequence continues, the total amount that will have been added to this savings account after five months is closest to
A.
B.
C.
D.
E.
PATTERNS, FUR1 2015 VCAA 1 MC
The first four terms in a geometric sequence are:
The fifth term in this sequence is
A.
B.
C.
D.
E.
PATTERNS, FUR 1 2006 VCAA 9 MC
A healthy eating and gym program is designed to help football recruits build body weight over an extended period of time.
Roh, a new recruit who initially weighs 73.4 kg, decides to follow the program.
In the first week he gains 400 g in body weight.
In the second week he gains 380 g in body weight.
In the third week he gains 361 g in body weight.
If Roh continues to follow this program indefinitely, and this pattern of weight gain remains the same, his eventual body weight will be closest to
A.
B.
C.
D.
E.
PATTERNS, FUR1 2006 VCAA 6 MC
A crystal measured 12.0 cm in length at the beginning of a chemistry experiment.
Each day it increased in length by 3%.
The length of the crystal after 14 days growth is closest to
A.
B.
C.
D.
E.
PATTERNS, FUR1 2006 VCAA 2 MC
The first three terms of a geometric sequence are
A possible value of
A.
B.
C.
D.
E.
PATTERNS, FUR1 2006 VCAA 1 MC
Which one of the following sequences shows the first five terms of an arithmetic sequence?
A.
B.
C.
D.
E.
PATTERNS, FUR1 2007 VCAA 9 MC
At the end of the first day of a volcanic eruption, 15 km2 of forest was destroyed.
At the end of the second day, an additional 13.5 km2 of forest was destroyed.
At the end of the third day, an additional 12.15 km2 of forest was destroyed.
The total area of the forest destroyed by the volcanic eruption continues to increase in this way.
In square kilometres, the total amount of forest destroyed by the volcanic eruption at the end of the fourteenth day is closest to
A.
B.
C.
D.
E.
PATTERNS, FUR1 2007 VCAA 7 MC
PATTERNS, FUR1 2007 VCAA 6 MC
In the first three layers of a stack of soup cans there are 20 cans in the first layer, 19 cans in the second layer and 18 cans in the third layer.
This pattern of stacking cans in layers continues.
The maximum number of cans that can be stacked in this way is
A.
B.
C.
D.
E.
PATTERNS, FUR1 2007 VCAA 2 MC
The yearly membership of a club follows an arithmetic sequence.
In the club’s first year it had 15 members.
In its third year it had 29 members.
How many members will the club have in the fourth year?
A.
B.
C.
D.
E.
PATTERNS, FUR1 2007 VCAA 1 MC
For the geometric sequence
the common ratio of the sequence is
A.
B.
C.
D.
E.
PATTERNS, FUR1 2008 VCAA 9 MC
When full, a swimming pool holds 50 000 litres of water.
Due to evaporation and spillage the pool loses, on average, 2% of the water it contains each week.
To help to make up this loss, 500 litres of water is added to the pool at the end of each week.
Assume the pool is full at the start of Week 1.
At the start of Week 5 the amount of water (in litres) that the pool contains will be closest to
A.
B.
C.
D.
E.
CORE*, FUR1 2008 VCAA 8 MC
When placed in a pond, the length of a fish was 14.2 centimetres.
During its first month in the pond, the fish increased in length by 3.6 centimetres.
During its
The maximum length this fish can grow to (in cm) is closest to
A. 14.4
B. 16.9
C. 19.0
D. 28.6
E. 17.2
CORE*, FUR1 2008 VCAA 7 MC
The sequence
A. fibonacci-related
B. arithmetic with
C. arithmetic with
D. geometric with
E. geometric with
PATTERNS, FUR1 2008 VCAA 6 MC
Kai commenced a 12-day program of daily exercise. The time, in minutes, that he spent exercising on each of the first four days of the program is shown in the table below.
If this pattern continues, the total time (in minutes) that Kai will have spent exercising after 12 days is
A.
B.
C.
D.
E.
PATTERNS, FUR1 2008 VCAA 5 MC
The first term of a geometric sequence is 9.
The third term of this sequence is 121.
The second term of this sequence could be
A.
B.
C.
D.
E.
PATTERNS, FUR1 2008 VCAA 3 MC
The values of the first seven terms of a geometric sequence are plotted on the graph above.
Values of
| (A) |
|
| (B) |
|
| (C) |
|
| (D) |
|
| (E) |
PATTERNS, FUR1 2008 VCAA 2 MC
For an examination, 8600 examination papers are to be printed at a rate of 25 papers per minute. After one hour, the number of examination papers that still need to be printed is
A.
B.
C.
D.
E.
PATTERNS, FUR1 2013 VCAA 9 MC
Eleven speed bumps are placed on a road.
The speed bumps are placed so that the distance between consecutive speed bumps decreases according to an arithmetic sequence.
The distance between the first and last speed bumps is exactly 100 m.
The smallest distance between consecutive speed bumps is 2 m.
The largest distance, in m, between two consecutive speed bumps is
A.
B.
C.
D.
E.
PATTERNS, FUR1 2013 VCAA 7 MC
The following are either three consecutive terms of an arithmetic sequence or three consecutive terms of a geometric sequence.
Which one of these sequences could not include 2 as a term?
A.
B.
C.
D.
E.
PATTERNS, FUR1 2009 VCAA 9 MC
There are 10 checkpoints in a 4500 metre orienteering course.
Checkpoint 1 is the start and checkpoint 10 is the finish.
The distance between successive checkpoints increases by 50 metres as each checkpoint is passed.
The distance, in metres, between checkpoint 2 and checkpoint 3 is
A.
B.
C.
D.
E.
PATTERNS, FUR1 2009 VCAA 5 MC
On Monday morning, Jim told six friends a secret. On Tuesday morning, those six friends each told the secret to six other friends who did not know it. The secret continued to spread in this way on Wednesday, Thursday and Friday mornings.
The total number of people (not counting Jim) who will know the secret on Friday afternoon is
A.
B.
C.
D.
E.
PATTERNS, FUR1 2009 VCAA 4 MC
The sum of the infinite geometric sequence 96, – 48, 24, –12, 6 . . . is equal to
A.
B.
C.
D.
E.
PATTERNS, FUR1 2009 VCAA 3 MC
The first four terms of a geometric sequence are 6400,
The value of
A.
B.
C.
D.
E.
PATTERNS, FUR1 2009 VCAA 2 MC
Each week a young boy saves an amount of his pocket money. The amount saved forms part of an arithmetic sequence. The table shows the amounts he saves in weeks 1 to 3.
If he continues to save in this way, the amount he will save in week eight is
A.
B.
C.
D.
E.
PATTERNS, FUR1 2011 VCAA 9 MC
A toy train track consists of a number of pieces of track which join together.
The shortest piece of the track is 15 centimetres long and each piece of track after the shortest is 2 centimetres longer than the previous piece.
The total length of the complete track is 7.35 metres.
The length of the longest piece of track, in centimetres, is
A.
B.
C.
D.
E.
PATTERNS, FUR1 2011 VCAA 8 MC
The first three terms of an arithmetic sequence are
The sum of the first
A.
B.
C.
D.
E.
PATTERNS, FUR1 2011 VCAA 6 MC
For which one of the following geometric sequences is an infinite sum not able to be determined?
A.
B.
C.
D.
E.
PATTERNS, FUR1 2011 VCAA 4 MC
The number of bees in a colony was recorded for three months and the results are displayed in the table below.
If this pattern of increase continues, which one of the following statements is not true.
A. There will be nine times as many bees in the colony in month 5 than in month 3.
B. In month 4, the number of bees will equal 270.
C. In month 6, the number of bees will equal 7290.
D. In month 8, the number of bees will exceed 20 000.
E. In month 10, the number of bees will be under 200 000.
PATTERNS, FUR1 2011 VCAA 2 MC
The first three terms of an arithmetic sequence are –3, –7, –11 . . .
An expression for the
A.
B.
C.
D.
E.
PATTERNS, FUR1 2014 VCAA 8 MC
The first term of a geometric sequence is
The common ratio of this sequence,
Which one of the following graphs best shows the first 10 terms of this sequence?
PATTERNS, FUR1 2014 VCAA 5 MC
Mary plans to read a book in seven days.
Each day, Mary plans to read 15 pages more than she read on the previous day.
The book contains 1155 pages.
The number of pages that Mary will need to read on the first day, if she is to finish reading the book in seven days, is
A.
B.
C.
D.
E.
PATTERNS, FUR1 2014 VCAA 3 MC
A city has a population of 100 000 people in 2014.
Each year, the population of the city is expected to increase by 4%.
In 2018, the population is expected to be closest to
A.
B.
C.
D.
E.
PATTERNS, FUR1 2014 VCAA 1-2 MC
Paul went running every morning from Monday to Sunday for one week.
On Monday, Paul ran 1.0 km.
On Tuesday, Paul ran 1.5 km.
On Wednesday, Paul ran 2.0 km.
The number of kilometres that Paul ran each day continued to increase according to this pattern.
Part 1
The number of kilometres that Paul ran on Thursday is
A.
B.
C.
D.
E.
Part 2
The total number of kilometres that Paul ran during the week is given by
A. the seventh term of an arithmetic sequence with
B. the seventh term of a geometric sequence with
C. the sum of seven terms of an arithmetic sequence with
D. the sum of seven terms of a geometric sequence with
E. the sum of seven terms of a Fibonacci-related sequence with
PATTERNS, FUR1 2011 VCAA 1 MC
Stefan swam laps of his pool each day last week.
The number of laps he swam each day followed a geometric sequence.
He swam 1 lap on Monday, 2 laps on Tuesday and 4 laps on Wednesday.
The number of laps that he swam on Thursday was
A.
B.
C.
D.
E.
PATTERNS, FUR1 2010 VCAA 9 MC
Before he began training, Jethro’s longest jump was 5.80 metres.
After the first month of training, his longest jump had increased by 0.32 metres.
After the second month of training, his longest jump had increased by another 0.24 metres.
After the third month of training, his longest jump had increased by another 0.18 metres.
If this pattern of improvement continues, Jethro’s longest jump, correct to two decimal places, will be closest to
A.
B.
C.
D.
E.
PATTERNS, FUR1 2010 VCAA 8 MC
PATTERNS, FUR1 2010 VCAA 5 MC
A team of swimmers was training.
Claire was the first swimmer for the team and she swam 100 metres.
Every other swimmer in the team swam 50 metres further than the previous swimmer.
Jane was the last swimmer for the team and she swam 800 metres.
The total number of swimmers in this team was
A.
B.
C.
D.
E.
PATTERNS, FUR1 2012 VCAA 8 MC
The graph above shows consecutive terms of a sequence.
The sequence could be
A. geometric with common ratio
B. geometric with common ratio
C. geometric with common ratio
D. arithmetic with common difference
E. arithmetic with common difference
PATTERNS, FUR1 2012 VCAA 7 MC
A dragster is travelling at a speed of 100 km/h.
It increases its speed by
- 50 km/h in the 1st second
- 30 km/h in the 2nd second
- 18 km/h in the 3rd second
and so on in this pattern.
Correct to the nearest whole number, the greatest speed, in km/h, that the dragster will reach is
A.
B.
C.
D.
E.
PATTERNS, FUR1 2012 VCAA 6 MC
The second and third terms of a geometric sequence are 100 and 160 respectively.
The sum of the first ten terms of this sequence is closest to
A.
B.
C.
D.
E.
PATTERNS, FUR1 2012 VCAA 5 MC
On the first day of a fundraising program, three boys had their heads shaved.
On the second day, each of those three boys shaved the heads of three other boys.
On the third day, each of the boys who was shaved on the second day shaved the heads of three other boys.
The head-shaving continued in this pattern for seven days.
The total number of boys who had their heads shaved in this fundraising activity was
A.
B.
C.
D.
E.
PATTERNS, FUR1 2012 VCAA 3-4 MC
Use the following information to answer Parts 1 and 2.
As part of a savings plan, Stacey saved $500 the first month and successively increased the amount that she saved each month by $50. That is, in the second month she saved $550, in the third month she saved $600, and so on.
Part 1
The amount Stacey will save in the 20th month is
A.
B.
C.
D.
E.
Part 2
The total amount Stacey will save in four years is
A.
B.
C.
D.
E.
PATTERNS, FUR1 2010 VCAA 4 MC
The first four terms of a geometric sequence are
The sum of the first ten terms of this sequence is
A.
B.
C.
D.
E.
PATTERNS, FUR1 2010 VCAA 3 MC
The prizes in a lottery form the terms of a geometric sequence with a common ratio of 0.95.
If the first prize is $20 000, the value of the eighth prize will be closest to
A.
B.
C.
D.
E.
PATTERNS, FUR1 2010 VCAA 2 MC
The first three terms of a geometric sequence are
The fourth term in this sequence would be
A.
B.
C.
D.
E.
PATTERNS, FUR1 2010 VCAA 1 MC
The sequence
could be
A. Fibonacci.
B. arithmetic.
C. geometric.
D. alternating.
E. decreasing.
PATTERNS, FUR1 2013 VCAA 6 MC
There are 3000 tickets available for a concert.
On the first day of ticket sales, 200 tickets are sold.
On the second day, 250 tickets are sold.
On the third day, 300 tickets are sold.
This pattern of ticket sales continues until all 3000 tickets are sold.
How many days does it take for all of the tickets to be sold?
A.
B.
C.
D.
D.
PATTERNS, FUR1 2013 VCAA 4 MC
The vertical distance, in m, that a hot air balloon rises in each successive minute of its flight is given by the geometric sequence
The total vertical distance, in m, that the balloon rises in the first 10 minutes of its flight is closest to
A.
B.
C.
D.
E.
PATTERNS, FUR1 2013 VCAA 3 MC
The first time a student played an online game, he played for 18 minutes.
Each time he played the game after that, he played for 12 minutes longer than the previous time.
After completing his 15th game, the total time he had spent playing these 15 games was
A.
B.
C.
D.
E.
PATTERNS, FUR1 2013 VCAA 2 MC
The graph above shows the first six terms of a sequence.
This sequence could be
A. an arithmetic sequence that sums to one.
B. an arithmetic sequence with a common difference of one.
C. a Fibonacci-related sequence whose first term is one.
D. a geometric sequence with an infinite sum of one.
E. a geometric sequence with a common ratio of one.
PATTERNS, FUR1 2013 VCAA 1 MC
The first three terms of an arithmetic sequence are 3, 5 and 7.
The ninth term of this sequence is
A.
B.
C.
D.
E.