Question

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

Answer 1

Answer:

$U_{n+1}=U_{n}-4$

Next term = -16

Step-by-step 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 :

$U_{6}=U_{5}-4 = -12-4=-16$