SOLUTION: if the fifth term of arithmetic sequence is 23 and the sum of the first ten terms of the sequence is 240 then wich of the following is the sum of the first sixty terms of this sequ

Question 1096566: if the fifth term of arithmetic sequence is 23 and the sum of the first ten terms of the sequence is 240 then wich of the following is the sum of the first sixty terms of this sequence?
A.2489
B.4440
C.1640
D.1980
Answer by ikleyn(52792) (Show Source): You can put this solution on YOUR website!
.

Notice that

   =

=  +  +  +  + .


Also notice that all 5 the sums in pairs are the same.

So, you actually have   = 240,  which implies

 =  = 48,  and then

 = 48,  which gives   = 48 - 23 = 25.


Thus the common difference is  d =  = 25-23 = 2.


Then   =  = 23 - 4*2 = 23 - 8 = 15.


So, the progression has the first term of 15 and the common difference of 2.


Then  = 15 + 2*59 = 133   and the sum of the first 60 terms is


 =  =  = (15+133)*30 = 4440.


Answer.   = 4440.  Option B).

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    - 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

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