Arithmetic, Geometric Sequences, Explicit, Recursive Formula

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 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 subsequent term in the sequence.

Front

How do you find the common ratio in a geometric sequence?

Back

The common ratio is found by dividing any term by the previous term in the sequence.

Front

What is the explicit formula for an arithmetic sequence?

Back

The explicit formula for an arithmetic sequence is t_n = a + (n-1)d, where a is the first term and d is the common difference.

Front

What is the explicit formula for a geometric sequence?

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The explicit formula for a geometric sequence is t_n = a * r^(n-1), where a is the first term and r is the common ratio.

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What is a recursive formula?

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A recursive formula defines each term of a sequence using the preceding term(s).

Front

Write the recursive formula for the arithmetic sequence 2, 5, 8, 11...

Back

a_n = a_{n-1} + 3, a_1 = 2.

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Write the recursive formula for the geometric sequence 3, 6, 12, 24...

Back

a_n = a_{n-1} * 2, a_1 = 3.

Front

What is the first term of the sequence defined by t_n = 5 + (n-1)2?

Back

The first term is 5.