Hannah W. answered • 05/29/15

Physics and Mathematics Tutor

4 is the first term (a), the ratio (r) between all of the terms is (1/2), and the last number of the term can also be represented as 1/16 = ar^(n-1). n being the number of term. We can solve for n to plug into our geometric sum equation. 1/16=(4)(1/2)^(n-1) solving for n gives us that n-1=6 so n=7.

The geometric equation is the sum = a[(1-r^n)/(1-r)]

sum= 4[(1-.5^7)/(1-.5)] = 7.9375 or 127/16.

A really helpful website for further explanation is:

http://www.mathsisfun.com/algebra/sequences-sums-geometric.html

Hope this helps!