SOLUTION: An Arithmetic Sequence has ten terms. The sum of the first three terms is 18 while the sum of the last three terms is 81. What is the sum of all ten terms?

Question 1083559: An Arithmetic Sequence has ten terms. The sum of the first three terms is 18 while the sum of the last three terms is 81. What is the sum of all ten terms?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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Then the second term is  = 6, while the 9-th term is  = 27 (why ?)

In other words, 

 = 6 = ,     (1)
 = 27 = .   (2)


Subtract (1) from (2) (both sides). You will get

7d = 27 - 6 = 21  --->  d =  = 3.

Hence,  = 6 - 3 = 3.   Also,  = 27+3 = 30.


Now, the sum of 10 terms is  =  =  = 33*5 = 165.

Answer. The sum of 10 terms is 165.

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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