How do I write a recursive formula for this sequence? 2, 6, 18, 54, 162, ... I already know the common difference is x3.

Question

Emmett Haynes

Mathematics

30 April, 18:19

How do I write a recursive formula for this sequence? 2, 6, 18, 54, 162, ... I already know the common difference is x3.

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Santos Reynolds · Answer 1

For the sequence 2, 6, 18, 54, ..., the explicit formula is: an = a1! rn"1 = 2! 3n"1, and the recursive formula is: a1 = 2, an+1 = an! 3. In each case, successively replacing n by 1, 2, 3, ... will yield the terms of the sequence. See the examples below.