Question

For whatvalue of n, are the n+n terms of two A.P's $63,65,67,.......and3,10,17,........equal$?

Answer 1

As we know that $n^{th}$ term in an A.P. is given as-

$a_n=a+(n-1)d$

Therefore,

For A.P. $63,65,67,.....$-

First term $\left(a\right)=63$

Common difference $\left(d\right)=65-63=2$

$a_n=63+(n-1)d$

For A.P. $3,10,17,.....$-

First term $\left(A\right)=3$

Common difference $\left(d\right)=10-3=7$

$a_n=3+(n-1)7$

Given that:-

$a_n=A_n$

$63+(n-1)2=3+(n-1)7$

$\Rightarrow 5(n-1)=60$

$\Rightarrow n-1=\frac{60}{5}$

$\Rightarrow n=12+1=13$

Hence the ${13}^{th}$ term of both A.P.'s will be equal.

Hence the correct answer is $13$.