Sequences

Front

What is a sequence in mathematics?

Back

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

Front

Define a recursive formula.

Back

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

Front

What is the first term of the sequence defined by the recursive formula g₁ = 2, g_n = 3 • g_n-1?

Back

The first term is 2.

Front

How do you find the first five terms of the sequence -24, -18, -12, -6, 0?

Back

The first five terms are obtained by following the pattern of adding 6 to the previous term.

Front

What is the recursive formula for the sequence 7, 14, 28, 56, 112?

Back

The recursive formula is a₁ = 7, a_n = a_n-1 • 2.

Front

How do you find the first four terms of the sequence defined by a_n = a_(n-1) - 18 where a₁ = 10?

Back

The first four terms are 10, -8, -26, -44.

Front

What is the common difference in the sequence 6, 17, 28, 39, 50?

Back

The common difference is 11.

Front

Write the recursive formula for the sequence 6, 17, 28, 39, 50.

Back

The recursive formula is a_n = a_n-1 + 11, a₁ = 6.

Front

What is the difference between an explicit formula and a recursive formula?

Back

An explicit formula provides a direct way to calculate the nth term, while a recursive formula defines terms based on previous terms.

Front

How can you identify the pattern in a sequence?

Back

To identify the pattern, look for consistent differences or ratios between consecutive terms.