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