Here are the first terms of an infinite geometric series.

Question

For each one, state whether or not it has a finite sum. If it does; find it.

 

a) 175, −70, 28, −11.2,....

 

b) −40, −50, −62.5, −78.125...

Answer 1

a) One can calculate the ratio of any term to its predecessor to get r, which in this case is -0.4 and therefore the infinite series converges

 

b) calculating the r value gives 5/4 > 1, so this infinite series diverges.

 

To find the sum in (a), use the formula S = a/(1-r)