Q30 of 176 Page 8

The sum of the 4th and Sth terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of A.P.

Given: a4 + a8 = 24


⇒ a +3d + a + 7d = 24


⇒ 2a + 10d = 24 …(i)


and a6 + a10 = 44


⇒ a +5d + a + 9d = 44


⇒ 2a + 14d = 44 …(ii)


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


2a + 10d – 2a – 14d = 24 – 44


⇒ –4d = – 20


⇒ d = 5


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


2a + 10×5 = 24


⇒ 2a + 50 = 24


⇒ 2a =24 –50


⇒ 2a =–26


⇒ a = –13


So, the first three terms are –13, –8, –3.


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