Question

A.P:11,6,-1,-4,... के कितने पदों का योग -360 है-​

Answer 1

A.P: The sum of how many terms of 11,6, 1, -4, ... is -360

$\textbf{Given:}$

$\text{A.P is 11,6,1,-4,.........}$

$\textbf{To find:}$

$\text{The number of terms should be added to get the sum -360}$

$\textbf{Solution:}$

$\text{In the given A.P, a=11, d=-5}$

$\text{We know that,}$

$\text{The sum of n terms of an A.P a, a+d, a+2d,.... is}$

$\boxed{\bf\,S_n=\frac{n}{2}[2a+(n-1)d]}$

$S_n=-360$

$\implies\,\frac{n}{2}[2a+(n-1)d]=-360$

$\implies\,\frac{n}{2}[2(11)+(n-1)(-5)]=-360$

$\implies\,n[22-5n+5]=-720$

$\implies\,n[27-5n]=-720$

$\implies\,27n-5n^2+720=0$

$\implies\,5n^2-27n-720=0$

$\implies\,5n^2-75n+48n-720=0$

$\implies\,5n(n-15)+48(n-15)=0$

$\implies\,(5n+48)(n-15)=0$

$\implies\bf\,n=15,\dfrac{-48}{5}$

$\therefore\textbf{15 terms should be added to get the -360}$