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Deepak Bora
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For what value of n, are the nth terms of two APs 63, 65, 67, and 3, 10, 17, … equal?

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The question is given from ncert Book of class 10th Chapter no. 5 Ex. 5.2 Q. 15. In the following question you have to find for what value of n, are the nth terms of two A.P is equal. Give the answer briefly.

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  1. Solution:

    Given two Arithmetic Progressions as; 63, 65, 67,… and 3, 10, 17,….

    By taking first Arithmetic Progression,

    63, 65, 67, …

    a = 63

    d = a2−a1 = 65−63 = 2

    The nth term of this A.P. = an = a+(n−1)d

    an= 63+(n−1)2 = 63+2n−2

    an = 61+2n ………………………………………. (i)

    By taking 2nd AP,

    3, 10, 17, …

    a = 3

    d = a2 − a1 = 10 − 3 = 7

    We know that,

    nth term of this A.P. = 3+(n−1)7

    an = 3+7n−7

    an = 7n−4 ……………………………………………………….. (ii)

    Given, nth term of these A.P.s are equal.

    Equating both these eq,

    61+2n = 7n−4

    61+4 = 5n

    5n = 65

    n = 13

    i.e The 13th terms of both these Arithmetic Progressions are equal.

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