Question

Write a recursive formula for the sequence 4, 0, -4, -8, -12, .... Then find the next term.

Answer 1

`U_(n+1)=U_(n)-4`

Next term = -16

Explanation:

`\text{let} \ \left( U_(n)\right) \text{be the sequence which we are looking for}`

0-4 = -4

(-4)-0 = -4

(-8)-(-4) = -4

(-12)-(-8) = -4

It’s clear that Un is an arithmetic sequence of common difference r = -4

Then

`U_(n+1)=U_(n)-4`

Next term :

`U_(6)=U_(5)-4 = -12-4=-16`