Q32 of 176 Page 8

Find the sum of 51 terms of the A.P. whose second term is 2 and the 4th term is 8.

Given: a2 = 2 and a4 = 8 and n = 51


We know that,


a2 = a + d = 2 …(i)


and a4 = a + 3d = 8 …(ii)


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


a + d – a – 3d = 2 – 8


⇒ -2d = -6


⇒ d = 3


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


a + 3 = 2


⇒ a = 2 – 3 = -1


Now, we have to find the sum of first 51 terms.





⇒ S51 = 51 [-1 + 25 × (3)]


⇒ S51 = 51 [74]


⇒ S51 = 3774


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