1)

a geometric series is one of the form:

where a is the first term, r is the common ratio and n is the current number of the term.

a)

we are given that the second term is 80,

we are also told that the fifth term is 5.12,

since

so the first term is 200, and the common ration is

b)

For a geometric series with , the sum to infinity is given by:

So here,

c)

The sum of the first terms of a geometric series is given by

So