Question

What is S5 for 1000 + 500 + 250 + ... ?

Answer 1

@stamp @PeterPan

Answer 2

This series is not like the series we had earlier, which was an arithmetic series... This is a new and more cunning type of series o.O

Answer 3

It is a pattern.

What is the pattern? Think different.

Answer 4

I'm trying to figure that pattern out

Answer 5

@Kayy_Drizzyy Take your time.

Answer 6

@Kayy_Drizzyy Hint: It is geometric. If you do not know what geometric sequence is, please open your textbook to the index, find the "geometric sequences" page number, and read the section.

Answer 7

Idk what the patterm is

Answer 8

is it \(S_5\) or is it
\[\sum_{n=0}^{\infty}1000\left(\frac{1}{2}\right)^n\]?

Answer 9

So my pattern is (1/2) ? right because i did 1000(1/2) and got my next answer which was 500

Answer 10

o.O
@Kayy_Drizzyy
Don't give up :)
Look at the second term, divide it by the first.
Look at the third term, divide it by the second.

Notice a pattern? :)

Answer 11

Oh you have it :)

Answer 12

The problem seems to go down not you means 100(1/2)=500 500(1/2)=250 250(1/2)=125 125(1/2)=62.5

Answer 13

My answer problem are large numbers . How do i get that answer

Answer 14

@satellite73

Answer 15

add

Answer 16

add by (1/2) ?

Answer 17

This is what is known as a Geometric Series....
Each term is just the previous term, multiplied to a constant known as...
...
the COMMON RATIO

Answer 18

\(S_5\) if i read it correctly means you have exactly 5 terms.
Add up the first five numbers

Answer 19

i know that but what am i adding by to get my S5 term ?

Answer 20

Which as you pointed out, is 1/2
Luckily, a formula exists for getting the sum of the first n-terms of a geometric series :)
\[\huge S_n = a\left( \frac{1-r^n}{1-r} \right)\]
Where as is your first term and r is your...
...
COMMON RATIO
>:D

Answer 21

I'm confused now

Answer 22

Well, what's your common ratio r? It's (1/2) right?

Answer 23

yes r is 1/2 but where does the A(1-1/2n) come from to get my answer ?

Answer 24

a is the very first term, which happens to be 1000 :)

Answer 25

and n is the number of terms you're adding, which happens to be 5.

Answer 26

okay so break it down to me so i can solve i it and get my answer.

Answer 27

\[\huge S_n = a\left( \frac{1-r^n}{1-r} \right)\]
You're taking the sum of the first 5 terms, so n=5

Answer 28

\[\huge S_5 = a\left( \frac{1-r^5}{1-r} \right)\]
Your series starts at 1000, so a = 1000

Answer 29

\[\huge S_5 = 1000\left( \frac{1-r^5}{1-r} \right)\]
And your common ratio is 1/2 = 0.5

Answer 30

\[\huge S_5 = 1000\left( \frac{1-\left(\frac{1}{2}\right)^5}{1-\frac{1}{2}} \right)\]
Now do the number-crunching :P

Answer 31

okay hold on

Answer 32

I still didnt get my answer from using my calc.

Answer 33

Try harder :D

Answer 34

I got my answer

Answer 35

What is it?

Answer 36

1937.5

Answer 37

Awesome, you got it!
Now, you could have gotten the same answer if you just keyed in
1000+500+250+125+62.5
:D

Answer 38

lol thank you

Answer 39

:)

Answer 40

I need more help in the future so stay online ill tag you in the problem i need help with, but thanks a lot.