Cheerleader Push-up Problem

[Guest]

Who can solve this?

Every time the football team scores a touchdown, the cheerleaders do a number of push-ups equal to the team’s current point total (7 for first TD, 14 for next one, 21 for next, etc.) Express as a formula the total number of push-ups the cheerleaders will do during the game for N touchdowns. Assume 7 points per touch down and that the team only scores via touchdown.

[Guest]

suppose there are [tex]n[/tex] touchdowns. so basically, we have to find

[tex]7+14+21+\ldots[/tex] upto [tex]n[/tex] terms. so this is an arithmetic progression and we have to find the sum of its first n terms.
[tex]\Longrightarrow7(1+2+3+\ldots+n)=\boxed{7\frac{n(n+1)}{2}}[/tex]