Q26 of 52 Page 1

Find the common difference of an A.P. whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.

Given,


a = 5


a1 + a2 + a3 + a4 = 1/2 (a5 + a6 + a7 + a8)


Therefore,


a + (a + d) + (a + 2d) + (a + 3d) = 1/2[(a + 4d) + (a + 5d) + (a + 6d) + (a + 7d)]


an = a(n – 1)d


Therefore,


4a + 6d = 1/2(4a + 22d)


8a + 12d = 4a + 22d


8a – 4a = 22d – 12d


4a = 10d ⇒ 4(5) = 10d


= 2


Therefore,


Common difference, d = 2


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