Question

the sum of how many terms of the AP 8, 6, 4, 2,....... is 18 ? state the reason for the double answer describe this question solution​

Answer 1

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

$\sf{The \ sum \ of \ 3 \ terms \ of \ AP \ is \ 18.}$

$\sf\orange{Given:}$

$\sf{The \ given \ AP \ is}$

$\sf{\implies{8, \ 6, \ 4, \ 2,…}}$

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

$\sf{Sum \ of \ how \ many \ terms \ is \ 18.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{The \ given \ AP \ is}$

$\sf{\implies{8, \ 6, \ 4, \ 2,…}}$

$\sf{Here, \ a=8, \ d=6-8=-2}$

$\boxed{\sf{Sn=\frac{n}{2}[2a+(n-1)d]}}$

$\sf{\therefore{18=\frac{n}{2}[2(8)+(n-1)(-2)]}}$

$\sf{\therefore{18=n[8+(n-1)(-1)]}}$

$\sf{\therefore{18=n[8-n+1]}}$

$\sf{\therefore{18=n[-n+9]}}$

$\sf{\therefore{18=-n^{2}+9n}}$

$\sf{\therefore{-n^{2}+9n-18=0}}$

$\sf{\therefore{-n^{2}+3n+6n-18=0}}$

$\sf{\therefore{-n(n-3)+6(n-3)=0}}$

$\sf{\therefore{(n-3)(-n+6)=0}}$

$\sf{\therefore{n=3 \ or \ -6}}$

$\sf{But, \ n \ can't \ be \ negative.}$

$\sf{\therefore{n=3}}$

$\sf\purple{\tt{\therefore{The \ sum \ of \ 3 \ terms \ of \ AP \ is \ 18.}}}$