Question

For what value of n, the nth terms of the sequences 3, 10, 17,... and 63, 65, 67,... are equal.

Answer 1

Given, the nth terms of the sequences 3, 10, 17,... and 63, 65, 67,... are equal.
since, nth term of A.P.= a + (n – 1) d
➪ 3+(n-1)7=63+(n-1)2
➪ 3 + 7n-7=63 + 2n-2
7n-2n= 61+4
5n = 65
n = 13
Therefore, 13^th terms of both these A.P.s are equal to each other.