Recursive and Explicit Formula Practice

Front

What is a recursive formula?

Back

A recursive formula defines the terms of a sequence using previous terms. For example, a_n = a_(n-1) + d, where d is the common difference.

Front

What is an explicit formula?

Back

An explicit formula defines the nth term of a sequence directly in terms of n. For example, a_n = a_1 + (n-1)d for an arithmetic sequence.

Front

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

Back

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

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount added to each term to get the next term. It can be found by subtracting any term from the term that follows it.

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How do you find the 25th term of the sequence if a_1 = 5 and d = 0.5?

Back

Using the formula a_n = a_1 + (n-1)d, a_25 = 5 + (25-1) * 0.5 = 17.

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What is the formula for the nth term of a geometric sequence?

Back

The nth term of a geometric sequence can be found using a_n = a_1 * r^(n-1), where r is the common ratio.

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

Back

The common ratio is found by dividing any term by the previous term. For example, in the sequence 3, 15, 75, the common ratio is 15/3 = 5.

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What is the common ratio for the sequence: 3, 15, 75...?

Back

The common ratio is 5.

Front

How do you find the 32nd term of the sequence 34, 37, 40, 43...?

Back

The common difference is 3. Using a_n = a_1 + (n-1)d, a_32 = 34 + (32-1) * 3 = 127.

Front

What is the formula to find the nth term of a linear sequence?

Back

The formula is a_n = a_1 + (n-1)d, where d is the common difference.