Q. 34 A4.0( 3 Votes )

# If the sum of 8 terms of an A.P. is 64 and the sum of 19 terms is 361, find the sum of n terms.

Given: S8 = 64 and S19 = 361

We know that,

64 = 4 [2a +7d]

16 = 2a + 7d …(i)

Now,

38 = 2a + 18d …(ii)

Solving linear equations (i) and (ii), we get

2a + 7d – 2a – 18d = 16 – 38

-11d = -22

d = 2 …(iii)

Putting the value of d in eq. (i), we get

2a + 7(2) = 16

2a = 16 – 14

2a = 2 …(iv)

Now, we have to find the Sn

[from (iii) and (iv)]

Sn = n [1 + n – 1]

Sn = n2

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