Question

What is the sum of the first n terms of this series?

4 + 6 + 8 + 10 + 12 + .....
HELP HELP HELP !!

Answer 1

Do you want a Σ (sigma notation) or with formula S(n) ?

Answer 2

sigma notation

Answer 3

Okay, can you (first) tell me the difference and the number of terms ?

Answer 4

8 ?

Answer 5

the difference or number of terms?

Answer 6

idk

Answer 7

The difference is equivalent to \(\large\color{blue}{a_n~-~ a_{n-1}}\), which is same as
\(\large\color{blue}{a_2~-~ a_{1}}\), and this is convertible to \(\large\color{blue}{6-4}\).

So, d=2.

Answer 8

The number of terms (appears to be) ∞

Answer 9

So on top of the notation you will have ∞.

Answer 10

and On the bottom (whatever you like) you can have n=1, or n=0
(which ever index you want, 1 or 0).

Answer 11

Can you think of some notation that will generate each term when you plug 1 for n, then 2 for n, then 3 for n, and on ?

Answer 12

2

Answer 13

\[\large\color{blue}{\sum_{n=0}^{∞}~~~~\rm{what~~do~~you~~think~~put~~here?}}\]

Answer 14

The difference is 2, you got that.

Answer 15

And a1= 4

Answer 16

The "slope" I would so call it, is 2, because hat you are having here is \(\large\color{blue}{y=2x+4}\)

Answer 17

let me know if you come up with something.