Sequences Flashcard 1

Front

What is a recursive formula?

Back

A recursive formula defines the terms of a sequence using previous terms. For example, in the sequence 17, 24, 31, 38, the recursive formula is a_n = a_{n-1} + 7, with a_1 = 17.

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. For example, the sequence 32, 20, 8, -4 is arithmetic with a common difference of -12.

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 nth term of a sequence?

Back

To find the nth term of a sequence, you can use either a recursive formula or an explicit formula that directly relates n to the term.

Front

What is the explicit formula for an arithmetic sequence?

Back

The explicit formula for an arithmetic sequence can be expressed as a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the explicit formula for the sequence 29, 34, 39, 44?

Back

The explicit formula is a_n = 29 + 5(n-1).

Front

What is the recursive formula for the sequence 17, 24, 31, 38?

Back

The recursive formula is a_n = a_{n-1} + 7, with a_1 = 17.

Front

What is the nth term of the sequence 3, -6, 12, -24, 48?

Back

The nth term is given by the formula a_n = 3(-2)^{(n-1)}.

Front

How do you determine if a sequence is arithmetic or geometric?

Back

To determine if a sequence is arithmetic, check if the difference between consecutive terms is constant. To determine if it is geometric, check if the ratio of consecutive terms is constant.

Front

What is the common difference in the sequence 32, 20, 8, -4?

Back

The common difference is -12.