SOLUTION: If the sum of the first 10 terms of an arithmetic progression is 4 times the sum of the first 5 terms, find the d in terms of a.

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Question 1108752: If the sum of the first 10 terms of an arithmetic progression is 4 times the sum of the first 5 terms, find the d in terms of a.
Answer by ikleyn(52903)   (Show Source): You can put this solution on YOUR website!
.
 = .    <<<---===  Standard formula for the sum of AP


 = .      <<<---===  Standard formula for the sum of AP


 =   is equivalent to


 = .


 = 


2a + 9d = 4a + 8d  ====>  9d - 8d = 4a - 2a  ====>  d = 2a.

Answer.   d = 2a  is the relation between  "d"  and  "a".

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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

into your archive and use when it is needed.


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