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Question
Write the first five terms of the following sequence and obtain the corresponding series:
a1 = 3, an = 3a(n - 1) + 2 for all n > 1
Solution
an = 3an−1 + 2 और a1 = 3
Putting n = 2, 3, 4, 5 in the sequence,
a2 = 3a1 + 2
= 3 × 3 + 2
= 11
a3 = 3a2 + 2
= 3 × 11+ 2
= 35
a4 = 3a3 + 2
= 3 × 35 + 2
= 107
a5 = 3a4 + 2
= 3 × 107 + 2
= 323
Hence, the first five terms of the sequence are 3, 11, 35, 107, and 323.
The corresponding series is 3 + 11 + 35 + 107 + 323 +...
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