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$=32$
 

Updated on: 10-Oct-2022

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