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. This difference is called the common difference (d).

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 (r).

Front

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

Back

To find the common difference (d), subtract any term from the subsequent term: d = a(n+1) - a(n).

Front

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

Back

To find the common ratio (r), divide any term by the previous term: r = a(n) / a(n-1).

Front

What is the next term in the arithmetic sequence: 2, 5, 8, 11...?

Back

The next term is 14 (common difference d = 3).

Front

What is the next term in the geometric sequence: 3, 6, 12, 24...?

Back

The next term is 48 (common ratio r = 2).

Front

Identify the type of sequence: 4, 8, 12, 16...

Back

This is an arithmetic sequence with a common difference d = 4.

Front

Identify the type of sequence: 5, 10, 20, 40...

Back

This is a geometric sequence with a common ratio r = 2.

Front

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

Back

The nth term (a_n) can be found using the formula: a_n = a_1 + (n-1)d.

Front

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

Back

The nth term (a_n) can be found using the formula: a_n = a_1 * r^(n-1).