Question

find the sum of this infinite geometric series: 100+60+36+...

Answer 1

It's fairly obvious to see that the common ratio is:\[\bf Common \ ratio = \frac{60}{100}=\frac{36}{60}=\frac{3}{5}\]So the geometric series is given by ('a' is the first term; 'r' is the common ratio):\[\bf ar^{n-1}=100\left( \frac{ 3 }{ 5 } \right)^{n-1}\]Since this geometric series is convergent, i.e. \(\bf |r| < 1\), the sum of the series is given by:\[\bf S_n=\frac{ a }{ 1-r }\]Can you evaluate the sum?

@mathisfun13

Answer 2

uhmm i think so

Answer 3

is the r my 3/5?

Answer 4

....

Answer 5

yes

Answer 6

so whats my Sn

Answer 7

I think the formula has already been neatly provided :)
\[\Large S_n=\frac{a}{1-r}\]
Where r is the common ratio and a is the first term in the series :)

Answer 8

ooh okay so 100 would be my a

Answer 9

correct

Answer 10

Yup :)

Answer 11

i got 250

Answer 12

Correct.