To get the next term do this:

Since a geometric sequence is a sequence, you find the terms exactly the same way that you do a sequence. n is our term number and we plug the term number into the function to find the value of the term.

So we have are formula to help us out (An = A1 ( R )^n-1). We can go directly to the next 1000 term with this formula. Example let's plug in the numbers for the next term after -1/4.

16 is the first term, -4 is the 2nd term, 1 is the 3rd term and -1/4 is the 4th term. Now let's get the 5th term.

16(-1/4)^5-1 = 16(-1/4)^4 = 1/16

All you have to do is plug in that term, lets plug in the 6 nth term and we get:

16(-1/4)^6-1 = 16(-1/4)^5 = -1/64

You see whats happening? The term gets smaller and smaller. It reminds me of limits in calculus. The 25th nth term would be 1/17592186044416.

For the nth term of the geometric sequence 16, - 4, 1, -1/4, ....

The ratio is -1/4

You would have to multiply -1/4 each time you go from one term to the next: (16)(-1/4) = - 4,

(- 4)(-1/4) = 1, and (1)(-1/4) = -1/4

R = ratio, A1 = First term, nth = General term

Here is the formula: An = A1 ( R )^n-1

Entering 16 for A1 and -1/4 for R we get:

An = 16 ( -1/4 )^n - 1