# Thread: Geometric Sequences - How to find maximum value

1. ## Geometric Sequences - How to find maximum value

This question legitimately confuses me.

I found that the formula for a geometric sequence is An=1800 x 0.9^(n-1)

How does one calculate the maximum value from that, however?
I do not understand how there is a maximum value for geometric sequences.

2. ## Re: Geometric Sequences - How to find maximum value

I think you mean a value which the sum of the sequence approaches but never reaches, called the sum to infinity. The formula ia a/(1-r)
So in your case a=1800 and r=0.9 so sum to infinity =1800/0.1 =18000. r has to be between -1 and +1 for a sequence to have a sum to infinity.

3. ## Re: Geometric Sequences - How to find maximum value

The maximum value of $a_n$ is simply the first term (assumed to be $a_1 = 1800$), because all proceeding terms get smaller.