Q18 of 47 Page 1

The sum of the first seven terms of an A.P. is 182. If its 4th and the 17th terms are in the ratio 1: 5, find the A.P.

Sum of n terms of an A.P. is given by,

S =


Sum of first 7 terms =


⇒ 182 = 7a + 21d


⸫ a + 3d = 26 …. (i)


Nth term of an A.P. is given by,


an = a + (n – 1) d


⇒ a4 = a + 3d


⇒ a17 = a + 16d


According to question,


⇒


⇒


⇒ 5a + 15d = a + 16d


⸫ d = 4a


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


⇒ a + 3 (4a) = 26


⇒ 13a = 26


⸫ a = 2


⸫ d = 8


⸫ The terms of the A.P. are 2, 10, 18, 26, 34, 42, 50, …., nth


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