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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.   `4300`

B.   `6870`

C.  `11\ 000`

D.  `11\ 290`

E.  `11\ 350`

Show Answers Only

`E`

Show Worked Solution

`text (GP where)\ \ \ T_2 = 100, and T_3 = 160` 

`:. r= T_3/T_2 = 160/100 = 1.6`

`T_2` `= ar`
`100`  `= a xx 1.6`
 `:. a` `= 62.5`

 

`text (Find)\ \ S_10`

`S_n` `= (a (r^n – 1))/ (r-1)`
`S_10` `= (62.5 (1.6^10 – 1))/(1.6 – 1)`
  `=11\ 349.07…`

`rArr E`