Q31 of 176 Page 8

Find the sum of first 21 terms of the A.P. whose 2nd term is 8 and 4th term is 14.

Given: a2 = 8 and a4 = 14 and n = 21


We know that,


a2 = a + d = 8 …(i)


and a4 = a + 3d = 14 …(ii)


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


a + d – a – 3d = 8 – 14


⇒ -2d = -6


⇒ d = 3


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


a + 3 = 8


⇒ a = 8 – 3 = 5


Now, we have to find the sum of first 21 terms.





⇒ S21 = 21 [5 + 10 × (3)]


⇒ S21 = 21 [35]


⇒ S21 = 735


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