Write the first five terms of the sequence and obtain the corresp… - Vidyadip

Question

Write the first five terms of the sequence and obtain the corresponding series a₁ = 3, a_n = 3a_n-1 + 2 for all n > 1

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Answer

Given: a₁ = 3, a_n-1 + 2 for all n > 1

Putting n = 2, 3, 4 and 5, we get

a₂ = 3a_2-1 + 2 = 3a_2-1 + 2 = 3a₁ + 2 = 3 $\times$ 3 + 2 = 9 + 2 = 11

a₃ = 3a_3-1 + 2 = 3a₂ + 2 = 3 $\times$ 11 + 2 = 33 + 2 = 35

a₄ = 3a_4-1 + 2 = 3a₃ + 2 = 3 $\times$ 35 + 2 = 105 + 2 = 107

a₅ 3a_5-1 + 2 = 3a₄ + 2 = 3 $\times$ 107 + 2 = 321 + 2 = 323

Hence the first five terms are 3,11,35,107,323.

Therefore, corresponding series is 3 + 11 + 35 + 107 + 323 + ……….

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