The fourth term of a geometric progression is 4 and the seventh term is 32/125. Find the first term, the common ratio and the sum of the first nth terms. Hence, deduce the sum to infinity.

common ratio is 2/5

First term is  125/2

The sum of the first n terms is:

The infinite sum is:

Step-by-step explanation:

The 4th term is 4, and the seventh term is 32/125 so we use the definition of nth term of a geometric sequence to create the following two equations:

Now we divide a7 by a4 to get rid of a1 and work on determining the common ratio of the sequence:

So, the common ratio is 2/5

we can now determine the first term:

The sum of the first n terms is given by the formula:

and therefore, the infinite sum is:

3x + 4y -25 =0 represents the amount of change sianna should recieve

47 - 90 = 43

43 - 180 = x

x = 137