Q33 of 176 Page 8

Find the sum of the first 25 terms of the A.P. whose 2nd term is 9 and 4th term is 21.

Given: a2 = 9 and a4 = 21 and n = 25


We know that,


a2 = a + d = 9 …(i)


and a4 = a + 3d = 21 …(ii)


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


a + d – a – 3d = 9 – 21


⇒ -2d = -12


⇒ d = 6


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


a + 6 = 9


⇒ a = 9 – 6 = 3


Now, we have to find the sum of first 25 terms.





⇒ S25 = 25 [3 + 12 × (6)]


⇒ S25 = 25 [75]


⇒ S25 = 1875


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