Arithmetic Sequences

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 (d) is the constant amount that each term increases or decreases by in an arithmetic sequence.

Front

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

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The nth term (a_n) can be found using 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 recursive formula for an arithmetic sequence?

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

Front

Given the sequence 3, 7, 11, 15, what is the common difference?

Back

The common difference is d = 4.

Front

Write the recursive formula for the sequence 10, 15, 20, 25...

Back

a_n = a_(n-1) + 5, a_1 = 10.

Front

What is the explicit formula for the arithmetic sequence 2, 5, 8, 11...?

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a_n = 2 + (n-1)3.

Front

If the first term of an arithmetic sequence is 5 and the common difference is -2, what is the 4th term?

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The 4th term is a_4 = 5 + (4-1)(-2) = -1.

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How do you determine if a sequence is arithmetic?

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A sequence is arithmetic if the difference between consecutive terms is constant.

Front

What are the first four terms of the sequence defined by a_n = a_(n-1) + 7, a_1 = 1?

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The first four terms are 1, 8, 15, 22.