Question

What is the explicit formula for this geometric sequence with recursive formula

Answer 1

C

generate the first few terms using the recursive formula

`a_(2)` = - 7 ×
`(1)/(3)` = -
`(7)/(3)`

`a_(3)` = -
`(7)/(3)` ×
`(1)/(3)` = -
`(7)/(9)`

`a_(4)` = -
`(7)/(9)` ×
`(1)/(3)` = -
`(7)/(27)`

r =
`a_(2)` /
`a_(1)` =
`(1)/(3)`

the n th term formula (explicit ) for a geometric sequence is

`a_(n)` =
`a_(1)`
`r^(n-1)` = - 7(
`(1)/(3)`)^(n - 1)

Answer 2

Option C

Explanation:

Given is a geometric sequence.

The recursive formula is given as

`a_n = (1)/(3) a_(n-1)`

Hence ratio of nth term to n-1th term

=
`(a_n)/(a_(n-1) ) =(1)/(3)`

`r=(1)/(3)`

I term =
`a_1=-7`

Hence explicit formula is

`a_n = -7((1)/(3) )^(n-1)`

Option C is right