If a_1=4a 1 =4 and a_n=-2a_{n-1}-2a n =−2a n−1 −2 then find the value of a_4a 4 .

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abidemiokin abidemiokin · Answer 1 · 2021-12-21T14:38:55+01:00

The 4th term of the sequence is -38

Given the following recursive function [tex]a_n=-2a_{n-1}-2[/tex] and, [tex]a_1=4[/tex], we need to get the fourth term of the sequence:

For the second term:

a2 = -2a1 - 2

a2 = -2(4) - 2

a2 = -8 - 2

a2 = -10

For the third term:

a3 = -2a2 - 2

a3 = -2(-10) - 2

a3 = 20 - 2

a3 = 18

For the fourth term:

a4 = -2a3 - 2

a4 = -2(18) - 2

a4 = -36 - 2

a4 = -38

Hence the 4th term of the sequence is -38

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