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# The 13th term of an AP is 4 times its 3rd term. If its 5th term is 16 then the sum of its first ten terms isA. 150B. 175C. 160D. 135

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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