The sum of the 5th and the 7th terms of an AP is 52 and the 10th term is 46. Find the AP.


Let the first term, common difference be a and d respectively.


As we know


an = a + (n - 1)d


and Given


a5 + a7 = 52


a + 4d + a + 6d = 52


2a + 10d = 52


a + 5d = 26


a = 26 - 5d [ eqn i]


also we have given


a10 = 46


a + 9d = 46


26 - 5d + 9d = 46 [ from eqn i]


4d = 46 - 26


4d = 20


d = 5


using this value in eqn I , we get


a = 26 - 5d


a = 26 - 5(5)


a = 1


as a = 6 and d = 5


So, required AP is a, a + d, a + 2d, a + 3d, …. i.e., 1, 1 + 5, 1 + 2(5), 1 + 3(5), …. i.e., 1, 6, 11, 16, …


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