Question

1. Find the first six terms of the recursively defined sequence Sn=3S(n−1)+2 for n>1, and S1=1...

1. Find the first six terms of the recursively defined sequence

Sn=3S(n−1)+2 for n>1, and S1=1

first six terms =

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Homework Answers

Answer #1

Sn = 3S(n-1) + 2 ; S1 = 1

n = 2

==> S2 = 3S(2-1) + 2

==> S2 = 3S1 + 2 = 3(1) + 2

==> S2 = 5

n = 3

==> S3 = 3S(3-1) + 2

==> S3 = 3S2 + 2 = 3(5) + 2

==> S3 = 17

n = 4

==> S4 = 3S(4-1) + 2

==> S4 = 3S3 + 2 = 3(17) + 2

==> S4 = 51 + 2

==> S4 = 53

n = 5

==> S5 = 3S(5-1) + 2

==> S5 = 3S4 + 2

==> S5 = 3(53) + 2

==> S5 = 159 + 2

==> S5 = 161

n = 6

==> S6 = 3S(6-1) + 2

==> S6 = 3S5 + 2

==> S6 = 3(161) + 2

==> S6 = 483 +2

==> S6 = 485

Therefore first six terms are 1, 5, 17, 53, 161, 485

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