Question

Two A.P.'s are given $9,7,5,$ ... and $24,21,18,$ ... If $n^{th}$ term of both the progressions are equal then find the value of $nand{n}^{th}$ term.

Answer 1

First A.P. is $9,7,5,.......$

Here,

First term, $a=9$

Common difference, $d=7-9=-2$

$n$th term, $a_n=a+(n-1)d$

$=9-2(n-1)$

$=11-2n$

Second A.P. is $24,21,18,.......$

Here,

First term, $a=24$

Common difference, $d=21-24=-3$

$n$th term, $a_n=a+(n-1)d$

$=24-3(n-1)$

$=27-3n$

$n$th term of both the progressions are equal, so

$11-2n=27-3n$

$-2n+3n=27-11$

$n=16$

$n$th term is $=11-2n$

$=11-32$

$=-21$