ACT Math · Sequences and series
A geometric sequence has first term 3 and common ratio 2. What is the 6th term?
A geometric sequence has first term 3 and common ratio 2. What is the 6th term?
Answer and explanation
Answer: C: 96
In a geometric sequence . With and , the sixth term is , choice C. Listing terms confirms it: . Choice D () uses an exponent of instead of , which is the seventh term. Choice B () is or , which does not follow the pattern. Choice A () is , treating the sequence as arithmetic-style multiplication by the term number. Remember that the exponent is one less than the term number.
More Sequences and series questions
- Question 59A sequence is defined by a_n = 3n - 2. What is a_10?
- Question 145An arithmetic sequence has first term 5 and common difference 3. What is the sum of the first 10…
- Question 189A sequence is defined recursively by a_1 = 4 and a_n = 2a_n-1 + 3. What is a_4?
- Question 237A theater has 20 seats in the first row. Each subsequent row has 4 more seats than the row before…
- Question 245A sequence is defined by a_1 = 100 and a_n = a_n-1 - 7. What is a_5?
Learn the method behind questions like this one
The ACT Math course teaches each tested skill through lessons, step-by-step solutions to sample problems, the complete study guide and full-length practice tests.