Question

Help With Sigma Notation

Answer 1

Use sigma notation to represent
3 + 6 + 9 + 12 + ...
for 28 terms.

Answer 2

\[\sum_{k=3}^{28}3(k-1)+3?\]

Answer 3

That is what I wrote on my notes but none of the answers have that.

Answer 4

3 + 6 + 9 + 12 + ...
can be written as
3(1) + 3(2) + 3(3) + 3(4) + ...

Do you see a nice easy way to write this as a sum? :)

Answer 5

What do you mean?

Answer 6

Like finite arithmetic equation to find the sum?

Answer 7

0_o whuu...

Answer 8

Lol. Do you mean An= An-1 +3 (a1=3)

Answer 9

You have this very complicated summation.
I'm trying to hint that it can be written in a very simple way,
if you can recognize the pattern.

Answer 10

\[\large\rm 3+6+9+12+...\]Can be written as,\[\large\rm 3(\color{orangered}{1})+3(\color{orangered}{2})+3(\color{orangered}{3})+3(\color{orangered}{4})+...\]

Answer 11

Oh sure, if you want to write it as arithmetic sequence, that's fine.
But simplify your expression.

3(k-1)+3
Distributing the 3,
3k-3+3

Answer 12

Alright. But how do I plug this in to the sigma notation?

Answer 13

You understand how to simplify further, yes?
the -3 and +3 cancel out.

So each term is of the form 3k,
where k counts from 1 to 28.

3(1) + 3(2) + 3(3)

Answer 14

Here is a quick example.
If I had 5+10,
Another way to write that is 5(1)+5(2)
Which is of the form 5k,
where k takes on the values 1 and 2.\[\large\rm 5+10=\sum_{k=1}^25k\]

Answer 15

Shouldn't 5 be on the bottom and 10 on the top?

Answer 16

5k is the "form" that each term takes on.
the numbers on the bottom and top are the counting numbers, the values we plug in for k.

Answer 17

Oh, so its not value, but location?

Answer 18

See how the bottom and top numbers are for counting? :D