Test questions on deriving and applying the sum of a finite geometric series.

📚 Quick Study Guide

• 🔢 A geometric series is a series where each term is multiplied by a constant, called the common ratio ($r$), to obtain the next term.
• 🧮 The sum of the first $n$ terms of a finite geometric series is given by: $S_n = a \frac{1 - r^n}{1 - r}$, where $a$ is the first term and $r$ is the common ratio (and $r \neq 1$).
• ➗ To find the common ratio ($r$), divide any term by its preceding term.
• 📝 If $|r| < 1$, the geometric series converges as $n$ approaches infinity. The sum to infinity is: $S = \frac{a}{1 - r}$.
• 💡 Remember to check if $r=1$. If so, $S_n = na$

✍🏼 Practice Quiz

1. What is the sum of the first 5 terms of the geometric series 2 + 6 + 18 + ...?
1. 60
2. 242
3. 244
4. 240
2. Find the sum of the geometric series: 1 + 1/2 + 1/4 + 1/8 + 1/16.
1. 31/16
2. 33/16
3. 35/16
4. 37/16
3. A geometric series has a first term of 3 and a common ratio of 2. What is the 6th term of the series?
1. 48
2. 96
3. 192
4. 160
4. What is the sum of the infinite geometric series: 4 + 2 + 1 + 1/2 + ...?
1. 6
2. 7
3. 8
4. 9
5. If the sum of an infinite geometric series is 10 and the first term is 2, what is the common ratio?
1. 4/5
2. 1/5
3. 2/5
4. 3/5
6. The 2nd and 4th terms of a geometric progression are 6 and 54 respectively. Find the first term if all the terms are positive.
1. 1
2. 2
3. 3
4. 4
7. A ball is dropped from a height of 16 meters. Each time it hits the ground, it bounces to 1/2 of its previous height. What is the total distance the ball travels?
1. 48
2. 32
3. 16
4. 64