SOLUTION: Find the sum of the first 196 terms of 2,7,12,17,.. I cant seem to figure this problem out

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Question 690880: Find the sum of the first 196 terms of 2,7,12,17,.. I cant seem to figure this problem out
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
If I say is the number of
the term of the sequence starting with zero, the
sequence looks like:

----------------
To get 196 terms, I want to let
run from to
Summing up the terms as I started doing, I have:
+ 5*( 0 + 1 + 2 + 3 + 4 + 5 + . . . + 195 )
-------------
The only difficult thing here is the summation in the parentheses
I recall that
( check it out )
So your summation is

Now I have

answer
------------------------------
I don't know any way to check the answer,
other than with some fancy calculator
or computer program.

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!
Find the sum of the first 196 terms of 2,7,12,17,.. I cant seem to figure this problem out

This is an arithmetic sequence, or A.P., and the formula for sum of an A.P.: , with , 1st term, or = 2; n, or amount of terms to be summed = 196, and d, or common difference = 5

Therefore, becomes:

, or sum of the 1st 196 terms in the series =

You can do the check!!

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