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

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

Mathematics
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post the screenshot please
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?
i dont know how to do screen shot

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thanks
okay now i know
each term is found by multiplying the previous term by -3
3*(-3) = -9 -9*(-3) = 27 27*(-3) = -81 etc etc
yeah
generate the first 8 terms, then add them up
okay hold on lets see
-4920
alternatively, you can use this formula \[\Large S_n = a*\frac{1-r^n}{1-r}\]
yeah thats what its says to use
yeah it's -4920
okay lets see ill send you a screen shot if its wrong okay
you are amazing
ok I'm glad that one worked
okay i have another
i have a question are you a teacher for algebra
because you seem to know what your doing
yes I've had lots and lots of practice
sweet heres the other question
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this is a geometric series what's the first term? common ratio?
1/3
first term = 1/3, yes
its going up in numerator x2 denomanator x3
common ratio = -2/3
okay
so its diverge
right
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
Rule: if |r| < 1, then the series converges otherwise, the series diverges
okay so its fixed sum is 1/5
if you generated all of the terms and added them up, they would add up to 1/5
okay
so converges are out right
what do you mean? I wrote above that the series converges
since |r|<1

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