Grade 9 Geometric Series Worksheet
This worksheet covers fundamental concepts and calculations related to geometric series for Grade 9 students.
Includes
Standards
Topics
Geometric Series Fundamentals
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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?
2, 4, 6, 8, ...
3, 6, 12, 24, ...
1, 2, 3, 4, ...
5, 10, 15, 20, ...
5. What is the common ratio of the sequence 81, 27, 9, 3, ...?
3
1/3
-3
-1/3
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.
True
False
9. A geometric sequence can have a common ratio of 0.
True
False
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).