Question

Verify that -130 is a term of the AP 11, 8,5,2, .... which term is this
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Answer 1

$\bold\red{\underline{\underline{Answer:}}}$

$\bold{-130 \ is \ the \ 48^{th} \ term \ of \ the}$

$\bold{given \ A.P.}$

$\bold\orange{Given:}$

$\bold{The \ given \ A.P. \ is }$

$\bold{=>11,8,5,2,…}$

$\bold\pink{To \ find:}$

$\bold{Which \ term \ is \ -130.}$

$\bold\green{\underline{\underline{Solution}}}$

$\bold{The \ given \ A.P. \ is }$

$\bold{=>11,8,5,2,…}$

$\bold{Here, \ a=11, \ d=8-11=-3}$

$\bold{Let, -130 \ be \ tn}$

$\bold{tn=a+(n-1)d... formula}$

$\bold{-130=11+(n-1)×(-3)}$

$\bold{\therefore{-3(n-1)=-130-11}}$

$\bold{-3n(n-1)=-141}$

$\bold{(n-1)=\frac{-141}{-3}}$

$\bold{n-1=47}$

$\bold{n=47+1}$

$\bold{n=48}$

$\bold\purple{\tt{\therefore{-130 \ is \ the \ 48^{th} \ term \ of \ the}}}$

$\bold\purple{\tt{given \ A.P.}}$