Q12 of 47 Page 1

The sum of the 5th and the 9th terms of an A.P. is 30. If its 25th term is three times its 8th term, find the A.P.

The formula to find the nth term of an A.P. is given by,

an = a + (n – 1) d


a5 = a + 4d …. (i)


a9 = a + 8d …. (ii)


Given, a5 + a9 = 30


⇒ a + 4d + a + 8d = 30


⸫ 2a + 12d = 30 …. (iii)


a25 = a + 24d


a8 = a + 7d


Given, a25 = 3a8


⇒ a + 24d = 3 (a + 7d)


⇒ a + 24d = 3a + 21d


⸫ 2a = 3d


Substituting the value 2a in eq (iii), we get


⇒ 3d + 12d = 30


⇒ 15d = 30


⸫ d = 2


⸫ a = 3


⸫ The terms of the A.P. are 3, 5, 7, 9, 11, 13, 15, 17, 19, 21,……. n terms


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