sequences and patterns

Front

What is a sequence in mathematics?

Back

A sequence is an ordered list of numbers that follow a specific pattern or rule.

Front

What is a pattern in a sequence?

Back

A pattern is a consistent rule or formula that defines how the numbers in a sequence are generated.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference (d) is the constant amount that is added or subtracted from one term to get to the next term in an arithmetic sequence.

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

What is a geometric sequence?

Back

A geometric sequence is a sequence 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

The common ratio (r) can be found by dividing any term by the previous term: r = a_n / a_(n-1).

Front

What is the formula for 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 first term of the sequence 2, 4, 8, 16, ...?

Back

The first term (a_1) is 2.

Front

What is the pattern for the sequence 2, 4, 8, 16, ...?

Back

The pattern is multiplying by 2.

Front

What is the fifth term of the arithmetic sequence 14, 24, 34, 44, ...?

Back

The fifth term is 54.