Arithmetic progression I'm studying for a test, and I am having a hard time with this particular exercise.
The first member is equal to 7 and the fifth member is equal to 59. 
How many members should be taken in to the sequence that it would amount to 24,217?
So far I have found out that d=13, but having trouble with the equation.
Any help would be appreciated. Thank you.

If the first number in an arithmetic progression is $a$ and the increment is $d$, term $i$ is $a+(i-1)d\ \ $.  So the sum of $n$ terms is $\sum_{i=1}^n a+(i-1)d=na+n(n-1)d/2\ \ $.  In your case, $a=7, d=(59-7)/4=13\ \ \ $, so you can just solve the quadratic equation $7n+13(n-1)n/2=24217\ \ $.
