Question

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

Answer 1

ANSWER

Explicit formula:

$a_n= 8n - 23$

Recursive

$a_{n}= a_{n - 1} + 8,a_1=-15$

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

$a_{n}= a_{n - 1} + 8,a_1=-15$