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A sequence is defined by a1=2 and an=3an-1+1. Find the sum a1+a2+⋯+an

A sequence is defined by a1=2 and an=3an-1+1. Find the sum a1+a2+⋯+an

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Answer #1

Answer:)

The given recurrence relation is :

This has the characteristic equation as :

Thus, the solution to the recurrence is as follows :

Now, since , we have :

Solving these equations gives us :

Thus, the full solution is :

Now, we need the sum:

Hence, using the formula for the geometric series, we get :

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