SOLUTION: Given an arithmetic progression 2, -1,-4,.., state three consecutive terms in this progression which sum up to -84.

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Question 1131474: Given an arithmetic progression 2, -1,-4,.., state three consecutive terms in this progression which sum up to -84.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

an arithmetic progression
, ,,....
first term:


=>common difference:
nth term:


then,








:
:
:
your sequence:
, , , , , , , , , , , , , , , , , ...
state three consecutive terms in this progression which sum up to :
The three consecutive terms are , , and .



then three consecutive terms are:
, ,
check:
Answer by ikleyn(52802)   (Show Source): You can put this solution on YOUR website!
.
Without any long computations, you must know that the middle term of the tree terms of an arithmetic progression, 

that sum up to -84,  is one third of -84, i.e.   = -28.


Since the common difference of the progression is -3, the terms are


    -25, -28, -31.

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Why it is so ?

Because if   (m-d),  m  and  (m+d)   are three consecutive terms of any  AP,  that sum up to S,  then 

    (m-d) + m + (m+d) = S   ====>   3m = S   ====>   m = .

-----------------

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

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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