SOLUTION: Use any suitable method to find the sum of 63+68+73+...+103+108

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Question 1056567: Use any suitable method to find the sum of
63+68+73+...+103+108

Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
Use any suitable method to find the sum of
63+68+73+...+103+108
~~~~~~~~~~~~~~~~~~~~~~~~~~

Arithmetic progression with the common difference 5.

The number of terms is %28108-63%29%2F5 + 1 = 10.

The sum is %28%2863%2B108%29%2F2%29%2A10 = 855.

I used the formula for the sum of an arithmetic progression.

See the lessons
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Use any suitable method to find the sum of
63+68+73+...+103+108
Number of terms (n) in the sequence: n+=+%28a%5Bn%5D+-+a%5B1%5D%29%2Fd+%2B+1, where:
a%5Bn%5D is the last term
a%5B1%5D is the 1st term
d is the common difference

n+=+%28a%5Bn%5D+-+a%5B1%5D%29%2Fd+%2B+1 now becomes: n+=+%28108+-+63%29%2F5+%2B+1_____n+=+%2845%2F5+%2B+1%29
n, or number of terms = 9 + 1, or 10
Sum of an AP formula: S%5Bn%5D+=+%28n%28a%5B1%5D+%2B+a%5Bn%5D%29%29%2F2
S%5B10%5D+=+%2810%28108+%2B+63%29%29%2F2____S%5B10%5D+=+5%28171%29
Sum of the AP, or highlight_green%28matrix%281%2C3%2C+S%5B10%5D%2C+%22=%22%2C+855%29%29