For what value of n, the nth terms of the arithmetic progressions andare equal?

Given, A.P. = 63, 65, 67,…

A.P.’ = 3, 10, 17,…


Let for A.P.,


First term, a = 63, d = 65 – 63 = 2


And nth term = an


an = 63 + (n – 1) 2


= 63 + 2n – 2


= 61 + 2n


For A.P.’


First term, a = 3, d = 10 – 3 = 7


nth term = an


Now nth term of both A.P. are equal


61 + 2n = -4 + 7n


7n – 2n = 61 + 4


n = 13


Hence, 13th term of both the A.P. are equal


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