Q. 324.8( 5 Votes )

# The 13th term of an AP is 4 times its 3rd term. If its 5th term is 16, find the sum of its first 10 terms.

Answer :

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

Given: a5 = 16

a13 = 4 a3

Now, Consider a5 = 16

a + (5 - 1)d = 16

a + 4d = 16 ………………….(1)

Consider a13 = 4 a3

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

a + 12d = 4a + 8d

3a - 4d = 0 ………………….(2)

Now, adding equation (1) and (2), we get,

4a = 16

a = 4

from equation (2), we get,

4d = 3a

4d = 12

d = 3

Now, Sum of first n terms of an AP is

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

Sum of first 10 terms is given by:

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

= 5 × [8 + 27]

= 5 × 35

= 175

S10=175

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