Question

Find Sn for the given arithmetic series.
a1= -100, d = –2, n = 21

Answer 1

`-2520`

Explanation:

For arithmetic series,
`S_n` means that sum of first n terms.

The formula is:

`S_n=(n)/(2)[2a_1+(n-1)d]`

Where

`a_1` is the first term (given as -100)

n is the number of terms (given as 21)

d is the common difference (given as -2)

So, we can plug in the values we know and find the sum of first 21 terms:

`S_n=(n)/(2)[2a_1+(n-1)d]\\S_(21)=(21)/(2)[2(-100)+(21-1)(-2)]\\S_(21)=10.5[-200+20(-2)]\\S_(21)=10.5[-240]\\S_(21)=-2520`

So the sum is -2520