Arithmetic and Geometric Sequences Test

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

How do you find the common difference in an arithmetic sequence?

Back

To find the common difference, subtract any term from the term that follows it. For example, in the sequence 2, 8, 14, the common difference is 8 - 2 = 6.

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 ratio in a geometric sequence?

Back

To find the common ratio, divide any term by the term that precedes it. For example, in the sequence 2, 6, 18, the common ratio is 6 / 2 = 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

Given the sequence 3, 6, 12, 24, what is the next term?

Back

The next term is 48, as each term is multiplied by 2 (common ratio of 2).

Front

What is the common difference in the sequence 5, 10, 15, 20?

Back

The common difference is 5.

Front

Identify the type of sequence: 400, 200, 100, 50, 25.

Back

This is a geometric sequence.

Front

What is the common ratio for the sequence 2, 6, 18, 54?

Back

The common ratio is 3.