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Question
If sn denotes the sum of first n terms of an A.P., whose common difference is d, then sn - 2sn−1 + sn−2 (n>2) is equal to
If sn denotes the sum of first n terms of an A.P., whose common difference is d, then sn - 2sn−1 + sn−2 (n>2) is equal to
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Solution
The correct option is C d
sn−2sn−1+sn−2=(sn−sn−1)−(sn−1−sn−2)
=an−an−1 [∵(sn−sn−1)=an]
=[a+(n−1)d]−[a+(n−2)d]
=a+nd−d−a−nd+2d
=d
sn−2sn−1+sn−2=(sn−sn−1)−(sn−1−sn−2)
=an−an−1 [∵(sn−sn−1)=an]
=[a+(n−1)d]−[a+(n−2)d]
=a+nd−d−a−nd+2d
=d
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