SOLUTION: The arithmetic progression consists of 15 terms. If the sum of the 3 terms in the middle is 27 and the sum of the last 3 terms is 18, then what is the sum of the first 3 terms?

Question 1083553: The arithmetic progression consists of 15 terms. If the sum of the 3 terms
in the middle is 27 and the sum of the last 3 terms is 18, then what is the
sum of the first 3 terms?
Answer by ikleyn(52790) (Show Source): You can put this solution on YOUR website!
.
The arithmetic progression consists of 15 terms. If the sum of the 3 terms
in the middle is 27 and the sum
of the last 3 terms is 18, then what is the sum of the first 3 terms?
~~~~~~~~~~~~~~~~~~~~~~~~~

"If the sum of the 3 terms in the middle is 27" then  =  = 9  (why ?)


Also, "if the sum of the last 3 terms is 18" then  =  = 6.


Thus you have 

 =  = 9     (1)   and

 =  = 6   (2) 


It implies that 6d = 6 - 9 = -3.   Hence,  d =  = -0.5.


Then  =  = 9 - 6*(-0.5) = 9 + 3 = 12.


Hence, the sum   = 36    (why ?)

Answer. 36.

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".

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