Question

Solve by unfolding: a0 = 2, and, for n > 0, an = 7an-1 + 3.
Hint: This one will involve applying the geometric sum formula

Answer 1

I got to 3 + 3(7) + 3(7^2) + 3(7^3)...+7^n x (2) but I can't seem to simplify....

Answer 2

assuming you are correct, use
\[1+7+7^2+...+7^n=\frac{7^{n+1}-1}{7-1}\]

Answer 3

So I would then have with my formula...
\[3(\frac{ 7^{n+1}-1 }{ 6}) + 2 (7^{n})\]

Answer 4

I think it needs simplified some more...

Answer 5

And are you sure it's not
\[3 (\frac{ 7^{n}-1 }{ 6 })\]