Thread: infinite geometric series

the sum of an infinite geometric series with first term a and common ratio r < 1 is given by.

$\displaystyle \frac{a}{1-r}$

The sum of a given infinite geometric series is $\displaystyle 200$, and the common ratio is$\displaystyle 0.15.$

What is the second term of this series?

by pluging the info given i got for an a value of $\displaystyle a=170$ which is not the value of the second term but that is where i don't understand how you find out what the second term is.

if

$\displaystyle \frac{a}{1-0.15} = 200$

then

$\displaystyle a=170$

the ans for the second term is $\displaystyle 25.5$ how did they get this. I looked at examples from several books but still ?

thnx ahead for help

Originally Posted by bigwave

the sum of an infinite geometric series with first term a and common ratio r < 1 is given by.

$\displaystyle \frac{a}{1-r}$

The sum of a given infinite geometric series is $\displaystyle 200$, and the common ratio is$\displaystyle 0.15.$

What is the second term of this series?

by pluging the info given i got for an a value of $\displaystyle a=170$ which is not the value of the second term but that is where i don't understand how you find out what the second term is.

if

$\displaystyle \frac{a}{1-0.15} = 200$

then

$\displaystyle a=170$

the ans for the second term is $\displaystyle 25.5$ how did they get this. I looked at examples from several books but still ?

thnx ahead for help

for any geometic series ...

$\displaystyle a_{n+1} = a_n \cdot r$

$\displaystyle a_2 = a_1 \cdot r = 170 \cdot 0.15 = 25.5$