Find a formula for the sum of the $n$ terms of the sequence:
$1, 1 + 2, 1 + 2 + 2^{2}, 1 + 2 + 2^{2} + 2^{3}, ...$
My Approach:
When $n$ increases the sequence increases by $2^{n}$ for every $n$.
I believe the formula has a constant which is $1$ based on the sequence pattern.
When I sum up the sequence for every $n$ it is $1, 3, 7, 15, ...$
I believe it is an arithmetic progression where $a = 1$ and $a(n) = 2a(n-1) + 3$
Although the formula is not quite correct i got some of the correct answers but not all
for every $n$.
Any help or hints would be appreciated for this
HINT: Partial sums of a geometric progression with parameters...