Q18 of 46 Page 1

The 13th term of an AP is four times its 3rd term. If its fifth term is 16, then find the sum of its first ten terms.

Let a be first term and d be common difference of AP.


As we know nth term of an AP is


an = a + (n - 1)d


Given


a13 = 4a3


a + 12d = 4(a + 2d)


a + 12d = 4a + 8d


3a - 4d = 0


3a = 4d ….[1]


Also given


a5 = a + 4d


16 = a + 4d


Multiplying both side by 3


48 = 3a + 4d


48 = 4d + 12d [By 1 ]


48 = 16d


d = 3


Also,


3a = 4d


3a = 4(3)


a = 4


As we know sum of first n terms of an AP is




S15 = 5(35) = 175


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