Sequences: Arithmetic, Geometric, Explicit and Recursive 2022

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in the sequence.

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

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which we multiply each term to get the next term in the sequence.

Front

What is the explicit formula for an arithmetic sequence?

Back

The explicit formula is a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the term number.

Front

What is the recursive formula for an arithmetic sequence?

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The recursive formula is a_n = a_(n-1) + d, with a_1 defined.

Front

What is the explicit formula for a geometric sequence?

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The explicit formula is a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.

Front

What is the recursive formula for a geometric sequence?

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The recursive formula is a_n = a_(n-1) * r, with a_1 defined.

Front

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

Back

Use the explicit formula: a_n = a_1 + (n-1)d.

Front

How do you find the nth term of a geometric sequence?

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Use the explicit formula: a_n = a_1 * r^(n-1).