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Find the eleventh term from the last term of the A.P. $27,\ 23,\ 19,\ ....,-65$
Given: AP: $27,\ 23,\ 19,\ ...,\ -65$.
To do: To find the eleventh term from the last term of the AP.
Solution:
AP is $27,\ 23,\ 19,\ .....,\ 65$
Here $a = 27,\ d =23-27=-4$
First we should find which term is $-65$,
Let $a_n=-65$
$\Rightarrow a+( n-1)d=-65$
On putting values
$\Rightarrow 27+( n-1)( -4)=-65$
$\Rightarrow 27+n( -4) -1( -4) =-65$
$\Rightarrow 27-4n + 4 =-65$
$\Rightarrow 31-4n =-65$
$\Rightarrow -4n = -65 -31$
$\Rightarrow -4n =-96$
$\Rightarrow n = \frac{96}{4}$
$\Rightarrow n = 24$
$11^{th}$ from last term =$( 24 -10)^{th}$ term=$14^{th}$ term from the first
We need to find out $a_{14}$
$a_n=a+( n-1)d$
On putting the values
$\Rightarrow a_{14}=27+( 14-1)( -4)$
$\Rightarrow a_{14}=27+( 13)( -4)=27-52=-25$
$\therefore 11^{th}$ term from the last $=$ $14^{th}$ term from the first $=25$.
Updated on: 10-Oct-2022
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