Arithmetic/Geometric Sequence

Front

What is an arithmetic sequence?

Back

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

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 common difference in an arithmetic sequence?

Back

The common difference can be found by subtracting any term from the subsequent term. For example, in the sequence 2, 5, 8, the common difference is 5 - 2 = 3.

Front

How do you find the common ratio in a geometric sequence?

Back

The common ratio can be found by dividing any term by the previous term. For example, in the sequence 3, 6, 12, the common ratio is 6 / 3 = 2.

Front

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

Back

Front

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

Back

Front

Identify the common difference in the sequence: 4, 7, 10, 13...

Back

The common difference is 3.

Front

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

Back

The common ratio is 3.

Front

Determine if the sequence 1, 4, 9, 16... is arithmetic or geometric.

Back

The sequence is neither arithmetic nor geometric; it is a sequence of perfect squares.

Front

What is the first term (a1) in the sequence: -6, -14, -22, -30...?

Back

The first term (a1) is -6.