How do you find the first five terms of each sequence a_1=0, a_(n+1)=-2a_n-4?

1 Answer
Jul 2, 2017

{0,4,-12,20,-44}

Explanation:

We have a sequence:

{a_n} = {a_1, a_2, a_3, ... }

Where:

\ \ \ \ a_1 =0
a_(n+1) = -2a_n-4

Put n=1 => a_2 = -2a_1 - 4
:. a_2 = -2(0) -4
" " = 0-4
" " = 4

Put n=2 => a_3 = -2a_2 - 4
:. a_3 = -2(4) - 4
" " = -8-4
" " = -12

Put n=3 => a_4 = -2a_3 - 4
:. a_4 = -2(-12) - 4
" " = 24-4
" " = 20

Put n=4 => a_5 = -2a_4 - 4
:. a_5 = -2(20) - 4
" " = -40-4
" " = -44

Thus the first five terms {a_1, a_2, a_3, a_5} of the sequence {a_n} are:

{0,4,-12,20,-44}