Q18 of 49 Page 1

The 8th term of an A.P. is equal to three times its third term. If its 6th term is 22, find the A.P.

The formula for nth term of an A.P. is given by,

an = a + (n – 1) d


⇒ a8 = a + 7d


⇒ a3 = a + 2d


⇒ a6 = a + 5d = 22 …. (i)


According to question,


a8 = 3a3


⇒ a + 7d = 3(a + 2d)


⇒ a + 7d = 3a + 6d


⇒ 2a = d


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


⇒ a + 5(2a) = 22


⇒ 11a = 22


⸫ a = 2


⸫ d = 4


⸫ The terms of the A.P. are 2, 6, 10, 14, 18, 22, ……..., nth


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