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PATTERNS, FUR1 2011 VCAA 8 MC

The first three terms of an arithmetic sequence are  `1, 3, 5 . . .`

The sum of the first  `n`  terms of this sequence, `S_n`, is

A.   `S_n = n^2`

B.   `S_n = n^2 - n`

C.   `S_n = 2n`

D.   `S_n = 2n - 1`

E.   `S_n = 2n + 1`

Show Answers Only

`A`

Show Worked Solution

`text(Sequence is  1, 3, 5 , . . .)`

♦ Mean mark 38%.
`text(AP where)\ \ \ a` `= 1, and`
`d` `= 3 – 1 = 2`
`S_n` `= n / 2 [ 2a + (n – 1) d ]`
  `= n / 2 [ 2 xx 1 + (n – 1) 2 ]`
  `= n / 2 [ 2 + 2n – 2 ]`
  `= n^2`

`=> A`

Filed Under: APs and GPs - MC Tagged With: Band 5

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