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Write first five terms of the sequence given by the rule a_n = (2n + 1) and obtain the corresponding series.
Solution:
We have, a_n = (2n + 1) ...... (1)
Putting n = 1, 2, 3, 4, 5, ..... successively in (1), we get precalculus tutorials
a₁ = (2 * 1 +1) = 3
a₂ = (2 * 2 +1) = 5
a₃ = (2 * 3 +1) = 7
a₄ = (2 * 4 +1) = 9
a₅ = (2 * 5 +1) = 11
Hence, the required sequence is 3, 5, 7, 9, 11, ......
The corresponding series is 3 + 5 + 7 + 9 + 11 + .....
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