Answer :

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


Given: a13 = 4(a3)


a5 = 16


To find: Sum of first ten terms.


Now, Consider a13 = 4a3


a + 12d = 4[a + 2d]


a + 12d = 4a + 8d


3a = 4d ………. (1)


Consider a5 = a + (5 - 1)d = 16


a + 4d = 16


a + 3a = 16 (from equation (1))


4a = 16


a = 4 ………. (2)


d = 3


Sum of n terms of an arithmetic series is given by:


Sn = [2a + (n - 1)d]


Therefore sum of 10 terms of the arithmetic series is given by:


S10 = [2(4) + (10 - 1)(3)]


= 5 × [8 + 27]


= 5 × 35


= 175

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