Question

What is the sum of the first 21 terms of this arithmetic series?
-5+(-3)+(-1)+1+...

Answer 1

Answer:

$S_{21}=315$

Step-by-step explanation:

The given arithmetic series is

-5+(-3)+(-1)+1+...

The first term of this series is

$a_1=-5$

The common difference is

$d=-3--5$

$d=-3+5$

$d=2$

The sum of the first n-terms of an arithmetic sequence is

$S_n=\frac{n}{2}(2a+d(n-1))$

$S_{21}=\frac{21}{2}(2(-5)+2(21-1))$

$S_{21}=\frac{21}{2}(-10+2(20))$

$S_{21}=\frac{21}{2}(-10+40)$

$S_{21}=\frac{21}{2}(30)$

$S_{21}=(21)(15)$

$S_{21}=315$

Answer 2

Answer:

The sum of the first 21 terms of this arithmetic series is 315.

Step-by-step explanation:

The given arithmetic series is

-5+(-3)+(-1)+1+...

Here first term is -5 and the common difference is

$d=-3-(-5)=2$

The sum of n terms of an AP is

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

We need to find the sum of the first 21 terms of this arithmetic series.

Substitute n=21, a=-5 and d=2 in the above formula, to find the sum of the first 21 terms of this arithmetic series.

$S_{21}=\frac{21}{2}[2(-5)+(21-1)(2)]$

$S_{21}=\frac{21}{2}[-10+40]$

$S_{21}=\frac{21}{2}(30)$

$S_{21}=315$

Therefore the sum of the first 21 terms of this arithmetic series is 315.