Question

What is the sum of the sequence?

Answer 1

Answer:

The sum of the sequence is -152250.

Step-by-step explanation:

Given : Sequence $-32+(-34)+(-36)+...+(-778)+(-780)$

To find : What is the sum of the sequence?

Solution :

The given sequence is in Arithmetic sequence as the difference between them is same.

Where, the first term is a=-32

The common difference is $d=a_2-a_1$

$d=(-34)-(-32)$

$d=-34+32$

$d=-2$

The last term is l=-780.

The last term formula is $l=a+(n-1)d$

$-780=-32+(n-1)(-2)$

$\frac{-780+32}{-2}=n-1$

$374=n-1$

$n=375$

The sum of n terms formula is

$S_n=\frac{n}{2}[a+l]$

$S_{375}=\frac{375}{2}[-32+(-780)]$

$S_{375}=\frac{375}{2}[-812]$

$S_{375}=375\times (-406)$

$S_{375}=-152250$

Therefore, the sum of the sequence is -152250.