SOLUTION: In an AP consisting of 15 terms, the sum of the last five terms is 305. If the sixth term is 26, find the sum of this AP
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Question 1140687: In an AP consisting of 15 terms, the sum of the last five terms is 305. If the sixth term is 26, find the sum of this AP Answer by ikleyn(52787) (Show Source):
The last five terms of this progression are , , , and .
The middle term of these 5 terms is , and it is equal to of the sum of that five terms.
It is the key point in the solution, and you should clearly understand it:
the average of any odd number of sequential terms of an AP is the middle term of this partial sequence.
Thus = = 61.
Now we know = 61 and = 26.
Between and , there are 13-6 = 7 gaps, each of which is equal to the common difference of the AP.
Hence, the common difference d = = = 5.
Then the first term is = - 5*5 = 26 - 25 = 1.
the 15-th term is = + (15-1)*d = 1 + 14*5 = 71.
Now the sum of the 15 terms of the AP is = = 540.
