Question

What is the sum of a 30-term arithmetic sequence where the first term is 74 and the last term is -100?



-468

-442

-416

-390

Answer 1

First of all, the sum of any given arithmetic sequence is:


\(\Large \color{MidnightBlue}{\Rightarrow {n \over 2}(a_{1} + a_{l}) }\)

n means the number of terms.
a1 means the first term.
aL means last term.

Answer 2

use \[s _{30}= \frac{30}{2}(74 + (-100))\]

Answer 3

That'll then become:


\(\Large \color{MidnightBlue}{\Rightarrow 15(74 - 100) }\)
\(\Large \color{MidnightBlue}{\Rightarrow 15(-26) }\)
\(\Large \color{MidnightBlue}{\Rightarrow -4090 }\)