Question

Complete the recursive formula of the geometric sequence -0.6.3, -15, 75, ....

c(1) =

c(n) = c(n − 1)*

Answer 1

`c(n)=-5c(n-1)\\c(1)=-0.6`

Explanation:

Given the geometric sequence

-0.6, 3, -15, 75, ...

Common ratio,
`r=(3)/(-0.6) =(-15)/(3)=-5`

The next term,
`c(n)` is obtained by multiplying the previous term c(n-1) by -5.

Therefore, the recursive formula for the sequence is:

`c(n)=-5c(n-1)\\c(1)=-0.6`