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# Find the $ 20^{\text {th }} $ term of the AP whose $ 7^{\text {th }} $ term is 24 less than the $ 11^{\text {th }} $ term, first term being 12.

Given:

The \( 7^{\text {th }} \) term of an AP is 24 less than the \( 11^{\text {th }} \) term and the first term is 12.

To do:

We have to find the \( 20^{\text {th }} \) term.

Solution:

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

This implies,

$a_1=a=12$

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

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

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

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

According to the question,

$a_7=a_{11}-24$

$a_{11}-a_7=24$

$a+10d-(a+6d)=24$ [From (i) and (ii)]

$10d-6d=24$

$4d=24$

$d=6$

Therefore,

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

$=12+19(6)$

$=12+114$

$=126$

Hence, the \( 20^{\text {th }} \) term of the AP is 126.

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