SOLUTION: what is the sum of the series 7+22+37...+292?

Question 1082123: what is the sum of the series 7+22+37...+292?
Found 2 solutions by Boreal, solver91311:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
It is (n/2)(a1+an)
n-1=285/15, the common difference=19
n=20
10*(7+292)=2990
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The sum of an arithmetic series is given by the sum of the first and last terms multiplied by the number of terms, quantity divided by two.

The first term is 7 and the last term is 292. The common difference is 22 minus 7 and 37 minus 22, namely 15. If you subtract 7 from 292 you get 285. 285 divided by 15 is 19, so 15 must have been added to 7 nineteen times to get from 7 to 292. Thus there are 20 terms, the 7 in the beginning and the nineteen 15s.

So:

You can do the arithmetic for yourself

John

My calculator said it, I believe it, that settles it

RELATED QUESTIONS
find the sum of 3799 and 292 (answered by Alan3354)
What is the sum me the series?... (answered by user_dude2008)
what is the sum of the last four terms of the series... (answered by Fombitz)
The sum of series... (answered by jim_thompson5910)
the sum of a number and 7 is... (answered by tommyt3rd)
Twice, the sum of my number and 7, minus 13 is 37.What is my number? (answered by checkley79)
Find the sum of n terms of the series 1+2+4+7+11+16++22+...+(nth... (answered by Edwin McCravy)
What is the sum of the finite arithmetic... (answered by ewatrrr)
what is the SUM OF A GEOMETRIC SERIES? (answered by Edwin McCravy)