Question

use the formula to evaluate the series
3-9+27-81+...-a8

Answer 1

post the screenshot please

Answer 2

there are 2 types of series arithmetic which has a common difference from one term to the next and the geometric progression that has a common ratio from on term to the next.
can you now identify what kind of series this is?

Answer 3

i dont know how to do screen shot

Answer 4

thanks

Answer 5

okay now i know

Answer 6

each term is found by multiplying the previous term by -3

Answer 7

3*(-3) = -9
-9*(-3) = 27
27*(-3) = -81
etc etc

Answer 8

yeah

Answer 9

generate the first 8 terms, then add them up

Answer 10

okay hold on lets see

Answer 11

-4920

Answer 12

alternatively, you can use this formula

\[\Large S_n = a*\frac{1-r^n}{1-r}\]

Answer 13

yeah thats what its says to use

Answer 14

yeah it's -4920

Answer 15

okay lets see ill send you a screen shot if its wrong okay

Answer 16

you are amazing

Answer 17

ok I'm glad that one worked

Answer 18

okay i have another

Answer 19

i have a question are you a teacher for algebra

Answer 20

because you seem to know what your doing

Answer 21

yes I've had lots and lots of practice

Answer 22

sweet heres the other question

Answer 23

this is a geometric series

what's the first term? common ratio?

Answer 24

1/3

Answer 25

first term = 1/3, yes

Answer 26

its going up in numerator x2 denomanator x3

Answer 27

common ratio = -2/3

Answer 28

okay

Answer 29

so its diverge

Answer 30

right

Answer 31

r = -2/3

since |r| < 1 is true, this means the infinite series does converge and there is a fixed sum it reaches

that sum would be

S = a/(1-r)
S = (1/3)/(1-(-2/3))
S = (1/3)/(5/3)
S = (1/3)*(3/5)
S = 1/5

Answer 32

Rule:
if |r| < 1, then the series converges
otherwise, the series diverges

Answer 33

okay so its fixed sum is 1/5

Answer 34

if you generated all of the terms and added them up, they would add up to 1/5

Answer 35

okay

Answer 36

so converges are out right

Answer 37

what do you mean? I wrote above that the series converges

Answer 38

since |r|<1