Grade 12 Math: Geometric Sequences Worksheet

Geometric Sequences: Grade 12 Math

Read each question carefully and answer to the best of your ability. Show all your work for full credit. This worksheet covers topics related to geometric sequences, including identifying the common ratio, finding specific terms, and calculating sums.

1. Which of the following sequences is a geometric sequence?

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

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

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

5. Find the 7th term of a geometric sequence where the first term is 5 and the common ratio is 2.

6. The third term of a geometric sequence is 18 and the sixth term is 486. Find the first term and the common ratio.

7. A sequence with a common difference is a geometric sequence.

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

9. Calculate the sum of the first 8 terms of the geometric sequence: 4, 12, 36, ...

10. An investment grows by 5% each year. If the initial investment is $1000, what will its value be after 10 years? (Hint: This is a geometric sequence problem.)