Question

Write an recursive formula for an, the nth term of the sequence 5, -1, -7,....

Answer 1

The terms of the sequence are 5, -1, -7

Let us find the common difference between each two consecutive terms

-1 - 5 = -6

-7 - (-1) = -7 + 1 = -6

Then the common difference is -6

The first term is 5

The recursive formula is

`a_1=1stterm;a_n=a_(n-1)+d`

Substitute in the formula the value of the 1st term and d the common difference

`a_1=5;a_n=a_(n-1)+(-6)`

Remember (+)(-) = (-)

`a_1=5;a_n=a_(n-1)-6`

This is the recursive formula for the sequence