If the $n$th terms of the two $APs$: $9, 7, 5, \ldots$ and $24, 21, 18, \ldots$ are the same,find the value of $n$. Also,find that term.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) For the first $AP$: $9, 7, 5, \ldots$
First term $a_1 = 9$,common difference $d_1 = 7 - 9 = -2$.
The $n$th term is $T_n = a_1 + (n - 1)d_1 = 9 + (n - 1)(-2) = 9 - 2n + 2 = 11 - 2n$.
For the second $AP$: $24, 21, 18, \ldots$
First term $a_2 = 24$,common difference $d_2 = 21 - 24 = -3$.
The $n$th term is $T_n = a_2 + (n - 1)d_2 = 24 + (n - 1)(-3) = 24 - 3n + 3 = 27 - 3n$.
Given that the $n$th terms are equal:
$11 - 2n = 27 - 3n$
$3n - 2n = 27 - 11$
$n = 16$.
Substituting $n = 16$ into either expression for the $n$th term:
$T_{16} = 11 - 2(16) = 11 - 32 = -21$.
Thus,the value of $n$ is $16$ and the term is $-21$.

Explore More

Similar Questions

Find the sum of multiples of $5$ lying between $84$ and $719$.

Two distinct terms of an $A.P.$ cannot be........

$3+6+9+12+\ldots+300 = \ldots$

For a given $A.P.$,$S_{10} = 50$ and $a = 0.5$. Then,$d = \ldots \ldots \ldots . .$

For an $A.P.$,the $5^{th}$ term is $30$ and the $12^{th}$ term is $100$. Find the sum of the first $20$ terms of the $A.P.$

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo