soumya_joy wrote:If the sum of the first 15 terms of an arithmetic progression equals that of the first 23
terms, then what is the sum of the first 38 terms?
A. -2 B. 0 C. 3 D. 5
Let the terms of the sequence be a�, a₂, a₃...
For the sum of the first 23 terms to be equal to the sum of the first 15 terms, the sum of terms a�₆ through a₂₃ must be 0.
For any arithmetic sequence, sum = (number of terms)(median).
Since a�₆ through a₂₃ is an arithmetic sequence composed of 8 terms whose sum is 0, we get:
0 = (8)(median)
median= 0.
a�₆ through a₂₃ are the 8 middle terms of a� through a₃₈.
Thus, the median of terms a�₆ through a₂₃ -- 0 -- is also the median of terms a� through a₃₈.
Thus:
Sum of the first 38 terms = (number)(median) = (38)(0) = 0.
The correct answer is
B.
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