Thread: Geometric Sequences 3

In 2004, wind turbines generated 326 MW of wind energy, and it is projected that the amount will be 10 000 MW per year by 2010. If this growth were modelled by a geometric sequence, determine the value of the annual growth from 2004 to 2010.

1 megawatt = 1,000,000 watts

My attempt: So, I think we solve for r (the ratio) so I plug in 10000=tn , 326=t1 , and 6 = n.
tn = (t1)(r^n-1)
10000 = (326)(r^6-1)
30.67484663 = r^5
1.98315 = r

The answer is 1.77; I was close... Can someone please tell me what I did wrong? Thanks!

The same mistake you made before: the formula, tn= (t1)(r^(n-1)) is valid if the initial value is "t1" then after the first year, you will have t2, the second year, t3, etc. You are numbering your years incorrectly.

Another way of handling that is to take the initial value to be "t0". Then you will have tn= (t0)(r^n).

I got the answer, I found out that n was suppose to be 7 not 6.