Question

If the sum of 8 terms of an AP is equal to the sum of 5 terms of the AP then the sum of 13 terms is​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{In an A.P}$

$\textsf{Sum of 8 terms=Sum of 5 terms}$

$\underline{\textsf{To find:}}$

$\textsf{Sum of 13 terms}$

$\underline{\textsf{Solution:}}$

$\underline{\mathsf{Formula\;used:}}$

$\textsf{The sum of first n terms of the A.P a,a+d,a+2d,............is}$

$\boxed{\mathsf{S_n=\dfrac{n}{2}[2a+(n-1)d]}}$

$\mathsf{As\;per\;given\;data,}$

$\mathsf{S_8=S_5}$

$\implies\mathsf{\dfrac{8}{2}[2a+(8-1)d]=\dfrac{5}{2}[2a+(5-1)d]}$

$\implies\mathsf{8[2a+7d]=5[2a+4d]}$

$\implies\mathsf{16a+56d=10a+20d}$

$\implies\mathsf{6a+36d=0}$

$\implies\mathsf{a+6d=0}$

$\mathsf{Now}$

$\mathsf{Sum\;of\;13\;terms}$

$\mathsf{S_{13}=\dfrac{13}{2}[2a+(13-1)d]}$

$\mathsf{S_{13}=\dfrac{13}{2}[2a+12d]}$

$\mathsf{S_{13}=\dfrac{13}{2}{\times}2[a+6d]}$

$\mathsf{S_{13}=13[0]}$

$\implies\boxed{\mathsf{S_{13}=0}}$

$\underline{\textsf{Find more:}}$

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Answer 2

Answer:

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