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In an A.P, the $1st$ term is $4$ and the $9th$ term is $20$. Then find the $15th$ term.
Given: In an A.P, the $1st$ term is $4$ and the $9th$ term is $20$.
To do: To find the $15th$ term.
Solution:
As given
$1st$ term$=4=a_1$
$9th$ term $=20=a_9$
we know, the formula for nth term of an A.P is $a_n=a_1+(n−1)d$ .....$( 1)$
Hence,
$a_9=a_1+(9−1)d$ ........from $( 1)$
$a_9=a_1+(8)d$
$20=4+8d$
$16=8d$
$d=2$
Therefore $a_{15}=a_1+(15−1)d$
$=a_1+(14)d$
$=4+14(2)$
$=28+4$
$=32$
$\therefore$ The $15th$ term of the A.P$=32$
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