SOLUTION: the first three terms of an arithmetic projection are x,2x+1 and 5x+1.find x and the sum of the first 10 terms

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Question 1110915: the first three terms of an arithmetic projection are x,2x+1 and 5x+1.find x and the sum of the first 10 terms
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
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(2x+1) -x = (5x+1) - (2x+1)    (<<<---===   -  =  - )

x + 1 = 3x

1 = 2x  ====>  x =  is the first term.


(2x+1) - x = (1+1) - 1/2 =  is the common difference.


The 10-th term is    +  =  = 14.


The sum of 10 terms = the average of the 1-st and the 10-th terms (which is equal to  = 7.25),  taken 10 times: 


Sum = 7.25*10 = 72.5.

Solved.

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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".


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Free of charge online textbook in ALGEBRA-II
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