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Which term of the AP 3, 15, 27, 34, …. will be 132 more than its 54th term?

1 Answer

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Best answer

Given,

AP is 3, 15, 25, 34, ……… . 

First term of AP is a = 3 

Common difference of AP is d = a2 – a1 = 15 – 3 = 12 

54th term of AP = a54 = a + (54 -1) d 

= 3 + 53 × 12 

= 3 + 636 = 639. 

(∵ a = 3 & d = 12) 

Let nth term of AP will be 132 more than its 54th term.

∴ an = 132 + 639 = 771. 

∴ a + (n – 1) d = 771 

(∵ an = a + (n – 1) d)

⇒ 3 + (n − 1)12 = 771 

(∵ a = 3 & d = 12) 

⇒ 12(n − 1) = 771 − 3 

= 768 

⇒ n − 1 = \(\frac{768}{12}\) = 64 

⇒ n = 64 + 1 

= 65. 

Hence,

65th term of given AP will be 132 more than its 54th term.

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