6 Questions
Which term best describes a sequence where each term is obtained by multiplying the previous term by a constant number?
Geometric sequence
What is the common ratio of a geometric sequence if the first term is 2 and the second term is 6?
3
If the first term of a geometric sequence is 3 and the common ratio is 0.5, what is the third term?
1.5
Which term best describes a sequence where each term is obtained by adding a constant number to the previous term?
Arithmetic sequence
What is the formula to find the nth term of an arithmetic sequence?
$a_n = a_1 + (n-1)d$
If the first term of an arithmetic sequence is 3 and the common difference is 4, what is the 6th term?
23
Study Notes
Geometric Sequence
- A geometric sequence is a sequence where each term is obtained by multiplying the previous term by a constant number.
- The common ratio of a geometric sequence can be found by dividing the second term by the first term.
- For example, if the first term is 2 and the second term is 6, the common ratio is 6/2 = 3.
- If the first term of a geometric sequence is 3 and the common ratio is 0.5, the third term is 3 × 0.5 × 0.5 = 0.75.
Arithmetic Sequence
- An arithmetic sequence is a sequence where each term is obtained by adding a constant number to the previous term.
- The formula to find the nth term of an arithmetic sequence is an = a1 + (n-1)d, where a1 is the first term and d is the common difference.
- For example, if the first term of an arithmetic sequence is 3 and the common difference is 4, the 6th term is 3 + (6-1)4 = 3 + 20 = 23.
Test your knowledge of geometric sequences with this quiz! Learn about the defining characteristics of geometric sequences and practice solving for terms and common ratios.
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