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11. Which term of the A.P. 3, 15, 27, 39,.. will be 132 more than its 54th term?

11. Which term of the A.P. 3, 15, 27, 39,.. will be 132 more than its 54th term?

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8741 Points
3 months ago
Given A.P. is 3, 15, 27, 39, … first term, a = 3 common difference, d = a2 − a1 = 15 − 3 = 12 We know that, an = a+(n−1)d Therefore, a54 = a+(54−1)d ⇒3+(53)(12) ⇒3+636 = 639 a54 = 639 We have to find the term of this A.P. which is 132 more than a54, i.e.771. Let nth term be 771. an = a+(n−1)d 771 = 3+(n −1)12 768 = (n−1)12 (n −1) = 64 n = 65 Therefore, 65th term was 132 more than 54th term. Or another method is; Let nth term be 132 more than 54th term. n = 54 + 132/2 = 54 + 11 = 65th term

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