SOLUTION: What is the sum of the first 50 terms of the arithmetic sequence in which the 3rd term is 10 and the 15th term is 22?

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Question 1084377: What is the sum of the first 50 terms of the arithmetic sequence in which the 3rd term is 10 and the 15th term is 22?
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
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a3%5D  = a%5B1%5D%2B2d  = 10     (1)
a%5B15%5D = a%5B1%5D%2B14d = 22     (2)


Subtract equation (1) from equation (2) (both sides). You will get

12d = 22 - 10 = 12.   Hence, d = 1.


Thus you found the common difference.  It is 1.


Then the first term of the AP is  a%5B1%5D = a%5B3%5D-2d = 10 - 2*1 = 8.


The last term of the AP is a%5B50%5D = a%5B1%5D+%2B+49%2Ad = 8 + 49*1 = 57.


Now you can find the sum of the first 50 terms of the AP as

S%5B50%5D = %28%28a%5B1%5D%2Ba%5B50%5D%29%2F2%29%2A50 = %28%288%2B57%29%2F2%29%2A50 = calculate.


On arithmetic progressions, see the lessons in this site:
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Mathematical induction and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".