Find the following sum:$ 1+(-2)+(-5)+(-8)+\ldots+(-236) $

Given:

\( 1+(-2)+(-5)+(-8)+\ldots+(-236) \)

To do:

We have to find the given sum.

Solution:

The given A.P. is \( 1+(-2)+(-5)+(-8)+\ldots+(-236) \).

Here,

$a_1=1, d=-2-1=-3$ 

We know that,

$a_n=a+ (n-1)d$

$S_n=\frac{n}{2}(a+l)$

This implies,

$l=a_n= 1 + (n-1)(-3)$

$-236= 1-3n+3$

$-236= 4-3n$

$3n= 4 + 236$

$3n =240$

$n = 80$

Therefore,

$S_n=\frac{80}{2}[1+(-236)]$

$=40(-235)$

$=-9400$

Therefore, \( 1+(-2)+(-5)+(-8)+\ldots+(-236)=-9400 \).

Tutorialspoint

Updated on: 10-Oct-2022

156 Views

Kickstart Your Career

Get certified by completing the course

Get Started