Question

For what value of n, are the $n^{th}$ terms of two A.Ps $63,65,67,....$ and $3,10,17,...$ equal?

Answer 1

Given,

$A.P{.}_1=63,65,67,\dots \dots ..$

$a=63,d=2$ and $t_n=63+(n–1)2$

$A.P{.}_2=3,10,17,\dots \dots ..$

$a=3,d=7$ and $t_n=3+(n–1)7$

Then according to the question,

nth of $A.P{.}_1$ = nth of $A.P{.}_2$

$63+(n–1)2=3+(n–1)7$

$60+2n–2=7n–7$

$58+7=5n$

$n=65/5=13$

Therefore, the $13th$ term of both the A.P.s is equal to each other.