Question

Find S20 for the series -1 + -3 + -5 + -7 +…

Answer 1

@Vocaloid

Answer 2

I have a feeling that \(S_{20}\) means the series [ie SUM] of the first 20 numbers in the sequence.

and not the 20th term of the sequence.

For the **given 4 terms**:

\(S_4 = -1 + -3 + -5 + -7\)

We can also say, reversing the order, that:

\(S_4 = -7 + -5 + -3 + -1\)

And then add them:

\(2 \times S_4 = -7 - 1 + -5 - 3 + -3 - 5 + -1 - 7 = -8 + -8 + - 8 + -8 = 4( - 8)\)

it's -16 all the way but they want \(S_{20}\)

so you work that out to \(S_{20}\), or generalise to \(S_n\)

...or you go look up a formula on Wiki for **arithmetic series**.

either gets you the answer :))