Q34 of 176 Page 8

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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