Arithmetic Vs 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. For example, 2, 4, 6, 8 is an arithmetic sequence with a common difference of 2.

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. For example, 3, 6, 12, 24 is a geometric sequence with a common ratio of 2.

Front

Identify the common difference in the arithmetic sequence: 5, 8, 11, 14.

Back

The common difference is 3.

Front

Identify the common ratio in the geometric sequence: 2, 6, 18, 54.

Back

The common ratio is 3.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term of an arithmetic sequence 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

What is the formula for the nth term of a geometric sequence?

Back

The nth term of a geometric sequence 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 kind of sequence is: 10, 20, 40, 80?

Back

Geometric.

Front

What kind of sequence is: 15, 12, 9, 6?

Back

Arithmetic.

Front

How do you find the next term in an arithmetic sequence?

Back

To find the next term in an arithmetic sequence, add the common difference to the last term.

Front

How do you find the next term in a geometric sequence?

Back

To find the next term in a geometric sequence, multiply the last term by the common ratio.