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# Question 12. If the nth term of the A.P. 9, 7, 5, …. is same as the nth term of the A.P. 15, 12, 9, … find n.

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This is the basic and conceptual question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise 9.4

In this question we have been given that the nth term of the A.P. 9, 7, 5, …. is same as the nth term of the A.P. 15, 12, 9, …

And we have to find n.

CBSE DHANPAT RAI publications
Class:- 10th
Understanding CBSE Mathematics
Question 12

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1. Solution:

Given that,

A.P1 = 9, 7, 5, …. and A.P2 = 15, 12, 9, …

nth term of the A.P1 = nth term of the A.P2,

As we know that, to find nth term in an A.P = a + (n – 1)d

For A.P1,

a = 9, d = Second term – first term = 9 – 7 = -2

And, its nth term an = 9 + (n – 1)(-2) = 9 – 2n + 2

an = 11 – 2n ———-(i)

Similarly, for A.P2

a = 15, d = Second term – first term = 12 – 15 = -3

And, its nth term an = 15 + (n – 1)(-3) = 15 – 3n + 3

an = 18 – 3n ——–(ii)

11 – 2n = 18 – 3n

n = 7

Hence, the 7th term of the both the A.Ps are equal.

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