For the regular sequence 1, 2, 3, ..., [tex]n[/tex], then sum is
[tex]\frac{n(n+1)}{2}[/tex]
If we multiply each number by 7 (7, 14, 21, ...), then the sum is
[tex]\frac{7n(n+1)}{2}[/tex]
and if we add 1 to each number (8, 15, 22, ...) then the sum is
[tex]\frac{7n(n+1)}{2}+n[/tex]
We have [tex]n=26[/tex] terms, so the sum is:
[tex]\frac{7(26)(27)}{2}+26[/tex]
[tex]=7(13)(27)+26[/tex]
[tex]=91(27)+26[/tex]
[tex]=2457+26[/tex]
[tex]=2483[/tex]
