Question

What is the sum of the arithmetic sequence 8, 15, 22 …, if there are 26 terms?

Answer 1

For the regular sequence 1, 2, 3, ..., $n$, then sum is
$\frac{n(n+1)}{2}$

If we multiply each number by 7 (7, 14, 21, ...), then the sum is
$\frac{7n(n+1)}{2}$
and if we add 1 to each number (8, 15, 22, ...) then the sum is
$\frac{7n(n+1)}{2}+n$

We have $n=26$ terms, so the sum is:
$\frac{7(26)(27)}{2}+26$
$=7(13)(27)+26$
$=91(27)+26$
$=2457+26$
$=2483$