Sequences and formulas REVIEW

Front

What is a sequence in mathematics?

Back

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

Front

How do you find the nth term of an arithmetic sequence?

Back

To find the nth term of an arithmetic sequence, use 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 common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term increases or decreases by in an arithmetic sequence.

Front

What is a recursive formula?

Back

A recursive formula defines the terms of a sequence using previous terms.

Front

Write the recursive formula for the sequence: 5, 8, 11, ...

Back

a_n = a_{n-1} + 3, a_1 = 5.

Front

What is an explicit formula?

Back

An explicit formula allows you to find the nth term of a sequence directly without needing to know the previous terms.

Front

Write the explicit formula for the sequence: 2, 8, 14, ...

Back

a_n = 6n - 4.

Front

How do you determine the 22nd term of the sequence: 5, 8, 11, ...?

Back

Use the formula: a_n = a_1 + (n-1)d. Here, a_1 = 5, d = 3, so a_{22} = 5 + (22-1)3 = 68.

Front

What is the first term of the sequence: 10, 5, 0, -5, ...?

Back

The first term, a_1, is 10.

Front

What is the common difference for the sequence: 10, 5, 0, -5, ...?

Back

The common difference is -5.