Question

Write an explicit formula for a of n, the nth term of the sequence 8, -24, 72, ...

Answer 1

`a_(n)` = 8
`(-3)^(n-1)`

Step-by-step explanat

There is a common difference r between consecutive terms, that is

r = - 24 ÷ 8 = 72 ÷ - 24 = - 3

This indicates the sequence is geometric with explicit formula

`a_(n)` = a
`(r)^(n-1)`

where a is the first term and r the common ratio

Here a = 8 and r = - 3 , thus

`a_(n)` = 8
`(-3)^(n-1)`