Question

Find the sum of the first 6 terms of the geometric series whose first term is 81 and whose common ratio is −2/3

Answer 1

48.5999?

Answer 2

Series is as follows:
81,-54,36,-2416,-10 2/3
Total is 44 1/3 or 133/3 or 43.3333

Answer 3

Thats -24,16

Answer 4

how u get that

Answer 5

series

Answer 6

You get the first number which is 81 and apply the ratio to each subsequent number

Answer 7

http://en.wikipedia.org/wiki/Geometric_series#Common_ratio

Answer 8

how do u apply it?

Answer 9

Ratios are multipliers

Answer 10

ok so multiply it by 81 then by that answer and so on tell i get to what?

Answer 11

So 81*(-2/3) = -54
That's number 2 in the series. Repeat:
54*(-2/3) = 36
Etc.

Answer 12

That's -54*(-2/3).
Damn typos :)

Answer 13

Then you tally the first 6 numbers in the series.

Answer 14

ok i got it i think check my answers i will post

Answer 15

Happy to see folks who want more than just an answer :)

Answer 16

haha cool happy to see folks that will help and not just talk all day on the chat lol

Answer 17

I'm supposed to be studying for my Chem and PolSci final. Distracting myself ;)

Answer 18

ha well ill get back with what i get for the next but dont let me get in your way :)

Answer 19

Geometric series:\[a+ar+ar^2...ar^n\]With a=81 and r=-2/3, The first six terms are:\[81+81(-2/3)+81(-2/3)^2...81(-2/3)^5\]This gives:\[81(1-2/3+4/9-8/27+16/81-32/243)\]Or,\[81(\frac{243-162+108-72+48-32}{243})=81\frac{133}{243}=\frac{10,773}{243}\]Or,\[\frac{3592}{81}\]

Answer 20

Check my arithmetic tho :)

Answer 21

ha

Answer 22

3591 on top :)

Answer 23

Eseidls expansion of the series is the best way to look at it. Depends on what math class you are in. For Calc 2 you'll want to be working through his process.

Answer 24

i got the check answer one up

Answer 25

agreed. I checked it using
http://www.analyzemath.com/Calculators_4/geometric_series_calc.html