Question

need help.

http://tinypic.com/r/219dhfs/5

Answer 1

I just want to make sure that \(\large S_3\) is referring to the sum of the first three terms of a geometric series with the given a and r?

Answer 2

yes

Answer 3

i substituted those numbers into the formula but I am just having a hard time solving it

Answer 4

Note that
\[\begin{aligned}\large S_3 &= 5 + 5\left(-\frac{2}{3}\right) + 5\left(-\frac{2}{3}\right)^2\\ &= 5-\frac{10}{3} + \frac{20}{9}\end{aligned}\]
All that's left now is to combine the three terms (by finding a common denominator) and simplify. Is the simplification where you're stuck now?

Answer 5

i got confused because the example shown to me on how to plug the numbers into the formula looks diff than what you showed me so i couldn't figure out how i was suppose to solve it

Answer 6

so would i turn the 5 into 5/1 and then find the cmd?

Answer 7

Ah, are you by any chance referring to the formula:
\[\large S_n = \sum_{k=1}^n ar^{k-1} = a\frac{1-r^n}{1-r}?\]
Doing things this way, you should see that
\[\large \begin{aligned} S_3 &= \sum_{k=1}^3 5\left(-\frac{2}{3}\right)^{k-1}\\ &= 5\cdot\frac{1-\left(-\dfrac{2}{3}\right)^3}{1-\left(-\dfrac{2}{3}\right)}\\ &= 5\cdot\frac{1+\dfrac{8}{27}}{\dfrac{5}{3}}\\ &= 5\cdot\frac{3}{5}\cdot\left(1+\frac{8}{27}\right)\\ &= 3\left(1+\frac{8}{27}\right)\\ &= 3+\frac{8}{9}\end{aligned}\]
At this point, you would go ahead and find a common denominator and simplify further. Does this make sense?

-----------------

In the way I showed, yes, you'd write \(\large 5=\dfrac{5}{1}\) and then find your common denominator.

I hope this is easy to follow! :-)

Answer 8

so when it says 1-(-2/3), do you just turn the two negative signs into a positive sign and leave it alone? I'm confused about that part. but i did solve it and got 35/9. thank you.

Answer 9

Whenever you take a number and subtract off a negative number, the two negatives make a positive and the result is an addition problem; i.e. \(\large a-(-b) = a+b\). Does this clarify things? :-)