SOLUTION: suppose A1=2 and A(n+1)=3A(n)+2. Write the first five terms of the sequence. Then write an explicit formula for An.

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Question 935569: suppose A1=2 and A(n+1)=3A(n)+2. Write the first five terms of the sequence. Then write an explicit formula for An.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
THAT makes better sense. Start at n=1, use the formula, and work forward.

A%5B2%5D=A%5B1%2B1%5D=3%2A2%2B2=highlight%288%29


A%5B3%5D=3%2A8%2B2=highlight%2826%29


A%5B4%5D=3%2A26%2B2=highlight%2880%29

You find the next three terms.



You also wanted to find the explicit formula.
On paper, the process of composing the first few successive terms is messy. I found for the fifth term, This:
A%5B5%5D=2%283%5E4%2B3%5E3%2B3%5E2%2B3%5E1%2B3%5E0%29
I can guess, if this remains workable, that the pattern is apparent. This seems to be based on the sum of a geometric sequence.
...
Fifth term should be 242.
I would guess along the apparent formula that the sixth term would be 728.