Question

A sequence is defined recursively by the formula f(n+1)=-2f(n). The first term of the sequence is -1.5. What is the next term in the sequence ?

Answer 1

given f(n+1) =-2f(n)
here f(n) =f(1) = -1.5
f(n+1) =f(2) = -2 * -1.5 = 3

Answer 2

The next term in the sequence is 3.

Explanation:

Given : A sequence is defined recursively by the formula
`f(n+1)=-2f(n)`. The first term of the sequence is -1.5.

To find : What is the next term in the sequence?

Solution :

The recursive formula is
`f(n+1)=-2f(n)`

We have given,
`f(1)=-1.5`

We have to find f(2)

So, Substitute n=1 in the recursive formula,

`f(1+1)=-2f(1)`

`f(2)=-2* (-1.5)`

`f(2)=3`

Therefore, The next term in the sequence is 3.