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.

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CCSS.HSF.BF.A.2

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.

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CCSS.HSF.BF.A.2

Front

How do you find the n^th term of an arithmetic sequence?

Back

The n^th term can be found using the formula: a_n = a₁ + (n-1)d, where a₁ is the first term and d is the common difference.

Tags

CCSS.HSF.BF.A.2

Front

Given the sequence 2, 9, 16, 23, what is the common difference?

Back

The common difference is 7.

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CCSS.HSF.BF.A.2

Front

What is the explicit formula for the arithmetic sequence 12, 10, 8, 6?

Back

The explicit formula is a_n = -2n + 14.

Tags

CCSS.HSF.BF.A.2

Front

Is the sequence 17, 9, 1, -7 arithmetic?

Back

Yes, the sequence is arithmetic because the difference between consecutive terms is constant (-8).

Tags

CCSS.HSF.BF.A.2

Front

Find the next three terms in the sequence 9, 19, 29, 39.

Back

The next three terms are 49, 59, 69.

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CCSS.HSF.BF.A.2

Front

What is the recursive formula for the sequence 2, 8, 14?

Back

The recursive formula is: a_n = a_n-1 + 6, with a₁ = 2.

Tags

CCSS.HSF.BF.A.2

Front

What does the term 'explicit formula' mean in the context of sequences?

Back

An explicit formula provides a direct way to calculate the n^th term of a sequence without needing to know the previous terms.

Tags

CCSS.HSF.BF.A.2

Front

What is the first term of the arithmetic sequence defined by a_n = 7n - 5?

Back

The first term (a₁) is 2.

Tags

CCSS.HSF.BF.A.2