Math Help - Need help with finding equal for geometric series

1. Need help with finding equal for geometric series

In 2004, US natural gas consumption was 646.7 billion cubic meters. Asian consumption was 367.7 billion cubic meters. During the previous decade, US consumption increased by 0.6% a year, while Asian consumption grew by 7.9% a year. Assume these rates continue into the future.

a) Give the first four terms of the sequence, an, giving US consumption of natural gas n years after 2003.

b) Give the first four terms of a similar sequence b_n showing Asian gas consumption.

I need some clarification. What do they mean n years after 2003. I want to put it in the formula (a_n) * (r)^(n-1).
a_n is initial
r is rate

So for a problem such as a), to find the a_n of 2003 do we multiply 646.7 by 0.006 to get 642.81?

So a formula for part a) should be: 642.81(1.006)^n-1?
Same thing with part b)

Please correct me if I am wrong. Thank you.

2. Originally Posted by florx

I need some clarification. What do they mean n years after 2003. I want to put it in the formula (a_n) * (r)^(n-1).
a_n is initial
r is rate
This sounds good. The year 2004 should be $n=1$ In this case.

Originally Posted by florx

So for a problem such as a), to find the a_n of 2003 do we multiply 646.7 by 0.006 to get 642.81?
Is this an increase?

Originally Posted by florx

So a formula for part a) should be: 642.81(1.006)^n-1?
Same thing with part b)
This is better, what do you get?

3. Originally Posted by pickslides

Is this an increase?

This is better, what do you get?

It is a decrease because the problem said that "During the previous decade, US consumption increased by 0.6% a year" so the US 2003's natural consumption should be less than 2004.

So is that formula I wrote correct?

4. Originally Posted by florx
giving US consumption of natural gas n years after 2003.
I understand "after 2003" to be 2004, 2005, 2006 and 2007.

Now use $646.7(1.006)^{n-1}$ where 2004 $\implies n=1$

5. Oh thank you so much for helping me. I misread the problem and thought they wanted the consumption of 2003 as a_n.