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प्रश्न
For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?
For what value of n, the nth term of A.P. 63, 65, 67, …….. and nth term of A.P. 3, 10, 17, …….. are equal to each other?
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उत्तर
Consider the A.P. 63, 65, 67, …
a = 63
d = a2 − a1 = 65 − 63 = 2
nth term of this A.P. = an = a + (n − 1)d
an = 63 + (n − 1)2
an = 63 + 2n − 2
an = 61 + 2n ...(1)
3, 10, 17, …
a = 3
d = a2 − a1
= 10 − 3
= 7
nth term of this A.P. = 3 + (n − 1) 7
an = 3 + 7n − 7
an = 7n − 4 ...(2)
It is given that the nth term of these A.P.s is equal to each other.
Equating both these equations, we obtain
61 + 2n = 7n − 4
61 + 4 = 5n
5n = 65
n = 13
Therefore, the 13th terms of both these A.P.s are equal to each other.
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