Question

F(n)=5 (2)^n-1 identify the first five terms if f(1) is the first term?

Answer 1

The first five terms are: 5,10,20,40,80

Explanation:

The given sequence is defined explicitly as:

`f(n) = 5( {2}^(n - 1) )`

We want to find the first five terms of this sequence:

For the first term, n=1,

`f(1) = 5( {2}^(1- 1) ) = 5 * {2}^(0) = 5`

When n=2,

`f(2) = 5( {2}^(2 - 1) ) = 5 * {2}^(1) = 10`

When n=3,

We have

`f(3) = 5( {2}^(3- 1) ) = 5 * {2}^(2) = 5 * 4 = 20`

When n=4, we get:

`f(n) = 5( {2}^(4- 1) ) = 5 * {2}^(3) = 40`

When n=5,

`f(5) = 5( {2}^(5- 1) ) = 5 * {2}^(4) = 5 * 16 = 80`

The first five terms are: 5,10,20,40,80