Find the 20^{text{th}} term of the AP whose 7 | vedclass

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(A) Let the first term be $a$ and the common difference be $d$ for an $AP$.Given that,the first term $a = 12$.According to the problem,the $7^{	ext{t

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$126$

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(A) Let the first term be $a$ and the common difference be $d$ for an $AP$.Given that,the first term $a = 12$.According to the problem,the $7^{	ext{th}}$ term $(T_7)$ is $24$ less than the $11^{	ext{th}}$ term $(T_{11})$.So,$T_7 = T_{11} - 24$.Using the formula for the $n^{	ext{th}}$ term of an $AP$,$T_n = a + (n-1)d$,we have:$a + 6d = (a + 10d) - 24$.Subtracting $a$ from both sides,we get $6d = 10d - 24$.Rearranging the terms,$4d = 24$,which gives $d = 6$.Now,we need to find the $20^{	ext{th}}$ term $(T_{20})$:$T_{20} = a + (20-1)d = a + 19d$.Substituting the values $a = 12$ and $d = 6$:$T_{20} = 12 + 19(6) = 12 + 114 = 126$.Thus,the $20^{	ext{th}}$ term of the $AP$ is $126$.

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 $12$.

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