Sequence Flex Review

Front

What is an Arithmetic Sequence?

Back

An Arithmetic Sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.

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 common difference in an Arithmetic Sequence?

Back

The common difference is found by subtracting any term from the term that follows it. For example, in the sequence 5, 8, 11, the common difference is 8 - 5 = 3.

Front

How do you find the common ratio in a Geometric Sequence?

Back

The common ratio is found by dividing any term by the term that precedes it. For example, in the sequence 2, 6, 18, the common ratio is 6 / 2 = 3.

Front

What is the explicit formula for an Arithmetic Sequence?

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The explicit formula for an Arithmetic Sequence 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 explicit formula for a Geometric Sequence?

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The explicit formula for a Geometric Sequence 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

Given the sequence 10, 7, 4, 1, what is the common difference?

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The common difference is -3, calculated as 7 - 10.

Front

Given the sequence 3, 9, 27, what is the common ratio?

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The common ratio is 3, calculated as 9 / 3.

Front

What is the first term of the sequence defined by a_n = 5n - 2?

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The first term (n=1) is a_1 = 5(1) - 2 = 3.

Front

What are the first four terms of the sequence defined by a_n = 2^n?

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The first four terms are 2, 4, 8, 16.