The sum of the first 77 terms of an arithmetic progression is the same as the sum of its first 99 terms.

What will be the sum of its first 176 terms?

Let a be the first term and d be the common difference.Now, we know that, sum of first n terms of an AP isSn = n22a + n-1dNow,S77 = 7722a + 76d = 77a + 38dS99 = 9922a + 98d = 99a + 49dNow, S77 = S99 77a + 38d = 99a + 49d7a+38d = 9a+49d7a + 266d = 9a + 441d2a = -175 d   ......1Now, S176 = 17622a + 175dS176 = 88-175d + 175d   using 1S176 = 0

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