The first term of an AP is 12 and its 7th term is 24 less than its 11th term. Find the 20th term of this AP.

Given:

The first term of an AP is 12 and its 7th term is 24 less than its 11th term.

To do:

We have to find the 20th term of this AP.

Solution:

Let the first term of the A.P. be $a$ and the common difference be $d$.

We know that,

nth term of an A.P. $a_n=a+(n-1)d$

Therefore,

$a_{1}=a=12$......(i)

$a_{7}=a+(7-1)d$

$=a+6d$.......(ii)

$a_{11}=a+(11-1)d$

$=a+10d$......(iii)

According to the question,

$a_{7}=a_{11}-24$

$a+6d=(a+10d)-24$

$10d+a-a-6d=24$

$4d=24$

$d=6$.....(iv)

$\Rightarrow a_{20}=a+(20-1)d$

$=12+19\times6$

$=12+114$

$=126$

The 20th term of the AP is $126$. 

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

66 Views

Kickstart Your Career

Get certified by completing the course

Get Started