Question

Question #08527

Answer 1

`81, -243, 729`

Explanation:

`1, -3, 9, -27`

this is an example of a geometric sequence, where one number is multiplied by a common ratio `r` to find the next number in the sequence.

here this is `-3`

`1 * -3 = -3`
`-3 * -3 = 9`
`9 * -3 = -27`

the general term for a geometric sequence is `ar^(n-1)`, where `a` is the starting term.

here, `a=1`

`ar^(n-1) = r^(n-1)`

`r = -3 -> r^(n-1) = -3^(n-1)`

the `n`th term is `-3^(n-1)`.
`a_n = -3^(n-1)`

for the next three terms in the sequence, `n = 5,6,7`

`a_n = -3^(n-1)`
`a_5 = -3^4 = 81`
`a_6 = -3^5 = -243`
`a_7 = -3^6 = 729`