If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, then find the sum of first 10 terms.


Let a and d be the first term and common difference, respectively of an AP


We know, Sum of first n terms of an AP




36 = 3[ 2a + 5d]


12 = 2a + 5d


2a = 12 - 5d [ eqn 1]


Now,



256 = 8[ 2a + 15d]


32 = 2a + 15d


32 = 12 - 5d + 15d [ using eqn 1]


20 = 10d


d = 2


using this value in eqn 1we get,


2a = 12 - 5(2)


2a = 2


a = 1


Now,



= 5(2 + 9(2))


= 5(20) = 100


So the sum of first 20 terms is 100


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