Question

What is the sum of the first five terms of a geometric series with a1 = 20 and r=1/4?

Below is my work:

The first term is 20
The second term is 20* 1/4 = 5
The third term is 5 * 1/4 = 5/4
The 4th term is 5/4 * 1/4 = 5/16
The 5th term is 5/16 * 1/4 = 5/64

Sum is therefore 20 + 5 + 5/4 + 5/16 + 5/64

= (1280 + 320 + 80 + 20 + 5) / 64

Express your answer as an IMPROPER FRACTION in LOWEST TERMS without using spaces.

Answer:
= 1705/64

I don't understand the improper fraction in lowest terms part please explain and let me know if im right. Thank you!

Answer 1

lowest terms the least numbers in the fraction eg 14/4 in lowest terms is 7/2
- because each number id divisible by 2

Answer 2

there are no common factors for 1705 and 64 so its in lowest terms already.
an improper fraction is one where the top part is greater than the bottom

Answer 3

Thank you. So my answer is correct does the math I did to solve this problem look correct for the question?

Answer 4

yes you have the correct answer - math is fine.

Answer 5

Thank you for your time and help. So 1705/64 it is :)

Answer 6

yes

Answer 7

yw