Q18 of 49 Page 1

The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.

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

an = a + (n – 1) d


⇒ a9 = a + 8d


⇒ a2 = a + d


⇒ a5 = a + 4d = 22 …. (i)


According to question,


⇒ a9 = 6a2


⇒ a + 8d = 6 (a + d)


⇒ a + 8d = 6a + 6d


⇒ 5a = 2d


Substituting the value of 2d in eq (i), we get


⇒ a + 2(5a) = 22


⇒ a + 10a = 22


⇒ 11a = 22


⸫ a = 2


⸫ d = 5


⸫ The terms of the A.P. are 2, 7, 12, 17, 22, 27, …., nth


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