Write the arithmetic series in Summation Notation.
4+8+12+16+20

Question

Write the arithmetic series in Summation Notation. 
4+8+12+16+20

bloomlocke367 · Answer

@iGreen @phi

phi · Answer

I would first factor 4 from each term, and write it as
4*(1+2+3+4+5)

bloomlocke367 · Answer

why?

phi · Answer

do you know how to write the sum of integers from 1 to 5 using the $\Sigma$ notation?

bloomlocke367 · Answer

Not really..

phi · Answer

did you study it at all?

bloomlocke367 · Answer

wait... 5 would go on the top, right? and n=1 on the bottom?

bloomlocke367 · Answer

and you took 4 out, so it would be 4n?

phi · Answer

yes.

phi · Answer

bloomlocke367 · Answer

it's n=1, because the lowest is 1? and 5 is on top because the upper limit is 5?

bloomlocke367 · Answer

The only reason I asked is because the text book doesn't have a good explanation.

phi · Answer

yes

bloomlocke367 · Answer

okay. Thanks.

phi · Answer

it's short-hand
$$ \Sigma_{n=1}^5 n = 1+2+3+4+5 $$
the idea is n starts at 1, goes up to 5
and we add up each term

phi · Answer

and for your problem, multiply by 4
$$ 4 \Sigma_{n=1}^5 n $$
or
$$  \Sigma_{n=1}^5 4n $$

bloomlocke367 · Answer

Oh, okay. That makes more sense. Thank you. :)

phi · Answer

yw