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Question from JP, a student:

Find the first five terms of a sequence with the nth term n^2+2n+1

and 2^n.

Thank You!

JP,

I am going to consider the sequence given by 3n2 + n - 1 for n = 1, 2, ...

To find the individual terms you substitute values for n.

Term n value
First 1 3 × 12 + 1 - 1 = 3
Second 2 3 × 22 + 2 - 1 = 13
Third 3 3 × 32 + 3 - 1 = 29
Fourth 4 3 × 42 + 4 - 1 = 51
Fifth 5 3 × 52 + 5 - 1 = 79

Thus the first 5 terms are 3, 13, 29, 51 and 79.

Penny

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