Unit 5 Sequences

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

How do you determine if a sequence is arithmetic, geometric, or neither?

Back

To determine the type of sequence, check the differences between consecutive terms for arithmetic (constant difference) or the ratios for geometric (constant ratio). If neither condition is met, the sequence is neither.

Front

What is the formula for the n-th term of an arithmetic sequence?

Back

The n-th term of an arithmetic sequence can be expressed as a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the formula for the n-th term of a geometric sequence?

Back

The n-th term of a geometric sequence can be expressed as a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

What is a common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term in an arithmetic sequence increases or decreases by.

Front

What is a common ratio in a geometric sequence?

Back

The common ratio is the fixed number that each term in a geometric sequence is multiplied by to get the next term.

Front

Find the next three terms in the arithmetic sequence: 5, 10, 15, ...

Back

20, 25, 30

Front

Find the next three terms in the geometric sequence: 3, 6, 12, ...

Back

24, 48, 96

Front

What is the explicit formula for the arithmetic sequence: 2, 5, 8, ...?

Back

a_n = 2 + (n-1)3