SOLUTION: Find the S20 if T3 = 19 and T8 = 44.

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Question 1109080: Find the S20 if T3 = 19 and T8 = 44.
Found 2 solutions by ikleyn, TeachMath:
Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
.
There are 8-3 = 5 common differences between T3= 19  and  T8= 44, i.e.


5d = 44 - 19 = 25  ====>  d = 25%2F5 = 5.


Hence,  T%5B1%5D = T%5B3%5D+-+2d = 19-2*5 = 9.


Then T%5B20%5D = T%5B1%5D%2B19%2A5 = 9 + 5*19 = 104.


It implies  S%5B20%5D = %28%28T%5B1%5D%2BT%5B20%5D%29%2F2%29%2A20 = %28%289%2B104%29%2F2%29%2A20 = 113*10 = 1130.

Solved.

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There is a bunch of lessons on arithmetic progressions 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".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

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Answer by TeachMath(96) About Me  (Show Source):
You can put this solution on YOUR website!
Sum of 1st 20 terms = 1,130