Grade 9 Geometric Series Worksheet

Geometric Series Fundamentals

Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. In a geometric sequence, each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common  .

2. The formula for the nth term of a geometric sequence is a_n = a_1 * r^( ).

3. A geometric series is the   of the terms of a geometric sequence.

4. Which of the following is a geometric sequence?

5. What is the common ratio of the sequence 81, 27, 9, 3, ...?

6. Find the 6th term of a geometric sequence where the first term is 5 and the common ratio is 2.

7. The first term of a geometric sequence is 4 and the common ratio is -3. Write out the first 4 terms of the sequence.

8. The sum of an infinite geometric series converges if the absolute value of the common ratio is greater than 1.

9. A geometric sequence can have a common ratio of 0.

10. Find the sum of the first 5 terms of the geometric series: 3 + 6 + 12 + ...

11. An initial investment of $1000 grows by 5% each year. How much will the investment be worth after 4 years? (Hint: This forms a geometric sequence where the common ratio is 1 + growth rate).