Infinite Geometric Series Worksheet with Answer Key

What's on the worksheet

1. Decide whether each infinite geometric series converges and give the sum if it does.
   64 + 48 + 36 + …10 - 4 + \dfrac{8}{5} - \cdots5 + \dfrac{15}{2} + \dfrac{45}{4} + \cdots\dfrac{1}{2} + \dfrac{1}{3} + \dfrac{2}{9} + \cdots4 - 5 + \dfrac{25}{4} - \cdots
2. Find each sum, naming the first term and ratio first.
   \sum_{k=1}^{\infty} 12\left(\dfrac{1}{4}\right)^{k-1}\sum_{k=1}^{\infty} 5\left(\dfrac{2}{3}\right)^{k}\sum_{k=3}^{\infty} \left(\dfrac{1}{2}\right)^{k}\sum_{n=1}^{\infty} \dfrac{2^{n}}{5^{n-1}}
3. Write each repeating decimal as an infinite geometric series and as a fraction.
   0.4\overline{6}0.1\overline{36}5.\overline{405}
4. Word problem: a town grant spent over and over at local shops.
5. Find the total of the areas or lengths in a pattern of squares joined at midpoints.
6. Find the ratio when the first term is 3 times the sum of all the other terms.