In an AP given a=7 and a_{13}=35,find d and S | vedclass

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(C) Given that,$a=7$ and $a_{13}=35$.We know the formula for the $n^{th}$ term of an $AP$ is $a_{n}=a+(n-1)d$.Substituting the values for $n=13$:$a_{1

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$273$

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(C) Given that,$a=7$ and $a_{13}=35$.We know the formula for the $n^{th}$ term of an $AP$ is $a_{n}=a+(n-1)d$.Substituting the values for $n=13$:$a_{13}=a+(13-1)d$$35=7+12d$$35-7=12d$$28=12d$$d=\frac{28}{12}=\frac{7}{3}$.Now,the formula for the sum of $n$ terms of an $AP$ is $S_{n}=\frac{n}{2}[a+a_{n}]$.For $n=13$:$S_{13}=\frac{13}{2}[a+a_{13}]$$S_{13}=\frac{13}{2}[7+35]$$S_{13}=\frac{13}{2}[42]$$S_{13}=13 	imes 21$$S_{13}=273$.

In an $AP$ given $a=7$ and $a_{13}=35$,find $d$ and $S_{13}$.

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