In an A.P, the $1st$  term is $4$ and the $9th$  term is $20$. Then find the $15th$.

Given: In an A.P, the $1st$  term is $4$ and the $9th$  term is $20$. 

To do: To find the $15th$.

Solution:

$1^{st}$ term $a_1=4$
​
$9^{th}$ term$=a_9=20$
​
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 $( 1)$

$\Rightarrow a_9=a_1+( 8)d$

$\Rightarrow 20=4+8d

$\Rightarrow 16=8d$

$\Rightarrow d=2$

Therefore, $a_{15}=a_1+(15−1)d$
       
$=a_1+( 14)d$

$=4+14( 2)$

$=28+4$

$=32$

$\therefore$ The $15^{th}$ term of the A.P$=32$.

Updated on: 10-Oct-2022

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