Arithmetic and Geometric 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 find the nth term of an arithmetic sequence?

Back

The nth term can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

How do you find the nth term of a geometric sequence?

Back

The nth term can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

What is the common difference in an arithmetic sequence?

Back

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

Front

What is the common ratio in a geometric sequence?

Back

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

Front

Is the sequence {3, 6, 12, 24, ...} arithmetic, geometric, or neither?

Back

Geometric, because each term is multiplied by 2 to get the next term.

Front

Is the sequence {10, 7, 4, 1, ...} arithmetic, geometric, or neither?

Back

Arithmetic, because the difference between consecutive terms is -3.

Front

What is the 5th term of the arithmetic sequence {2, 5, 8, 11, ...}?

Back

The 5th term is 14.

Front

What is the 4th term of the geometric sequence {5, 15, 45, ...}?

Back

The 4th term is 135.