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Find the $9$ term from the end $( towards\ the\ first\ term)$ of A.P. $5,\ 9,\ 13,\ .......\ 185$.
Given: An A.P. $5,\ 9,\ 13,\ .......\ 185$.
To do: To find the $9^{th}$ term from end.
Solution:
Given A.P. is $5,\ 9,\ 13,\ ....\ 185$
To find the $9^{th}$ term from end:
On rearranging the A. P.
$185,\ 181,\ ......,\ 13,\ 9,\ 5$
First term $=a=185$
Common difference $=d=a_2-a_1=181-185=-4$
$n^{th}$ term in an A. P $=a_n=a+( n-1)d$
$a = 185$; $d=-4;$ $n=9$
$9^{th}$ term$=a_9=a+( 9-1)d$
$=185+8\times( - 4)$
$=185-32$
$=153$
Therefore required $9^{th}$ term from the end$=153$.
Updated on: 10-Oct-2022
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