Write down the first five terms of the following recursively

Write down the first five terms of the following recursively defined sequence.

Solution

if a₁=1 and a_n+1=-2a_n-8

nowby placing n=1

a₁₊₁=-2(1)-8=-10=a₂

similarly by placing n=2

a₂₊₁=-2(-10)-8=12=a₃

now n=3

a₃₊₁=-2(12)-8=-32=a₄

now n=4

a₄₊₁=-2(-32)-8=56=a₅

now n=5

a₅₊₁=-2(56)-8=-120=a₆