Question

Write the recursive formula and the explicit formula for the sequence {-15,-7,1,9, 17,...}.

Answer 1

Explicit formula:

`a_n= 8n - 23`

Recursive

`a_(n)= a_(n - 1) + 8,a_1=-15`

Step-by-step explanation

The first term of the sequence is

`a_1=-15`

The common difference is

`d = - 7 - - 15`

`d = 8`

The nth term is given by the formula,

`a_n=a_1 + d(n - 1)`

`a_n= - 15+ 8(n - 1)`

`a_n= - 15+ 8n -8`

The explicit formula is;

`a_n= 8n - 23`

The recursive definition is

`a_(n)= a_(n - 1) + 8,a_1=-15`