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The thirteenth term of an AP is 4 times its 3rd term. If its 5th term is 16, find the sum of its first 10 terms from the choices given below.

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125

150

175

200

answer is C.

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Detailed Solution

It is given that the 13th term is 4 times its 3rd term. And its 5th term is 16.
From the given information,

a 13 = 4 a 3

.
The nth term of an AP is given by,

a n = a + (n − 1) d

.
Substitute the known values in the formula,

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

3 a = 4 d

……(1)
Given,

a 5 = 16

a + 4 d = 16

……(2)
Substitute equation (1) in (2),

4 a = 16

a = 4

The first term is 4.
Substitute a in equation (1) to find the value of d.

3 (4) = 4 d

d = 3

The formula gives the sum of the terms,

S n = n 2 [2 a + (n − 1) d]

.
Substitute the known values in the formula,

S 10 = 102 [2 (4) + (10 − 1) 3]

= 5 [8 + 27]

= 175

The sum of the terms is 175.
Hence, option 3) is correct.

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