Arithmetic Sequence Finding the nth term

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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

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What is the formula for the nth term of an arithmetic sequence?

Back

The nth term of an arithmetic sequence 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.

Tags

CCSS.HSF.BF.A.2

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Find the 64th term for the sequence defined by \( a_n = 5n + 4 \).

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The 64th term is \( a_{64} = 5(64) + 4 = 320 + 4 = 324 \).

Tags

CCSS.HSF.BF.A.2

Front

Use the explicit formula to find the 7th term of the sequence \( a_n = 22 - 3(n-1) \).

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The 7th term is \( a_7 = 22 - 3(7-1) = 22 - 18 = 4 \).

Tags

CCSS.HSF.BF.A.2

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What are the next two terms in the sequence 4, 7, 10, 13?

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The next two terms are 16 and 19.

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CCSS.HSF.BF.A.2

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Find the next three terms in the arithmetic sequence: 25, 34, 43, 52, ...

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The next three terms are 61, 70, 79.

Tags

CCSS.HSF.BF.A.2

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

Back

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

Tags

CCSS.HSF.BF.A.2

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What is the common difference in the arithmetic sequence 10, 15, 20, 25?

Back

The common difference is 5.

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CCSS.HSF.BF.A.2

Front

How do you determine if a sequence is arithmetic?

Back

A sequence is arithmetic if the difference between any two consecutive terms is the same.

Tags

CCSS.HSF.BF.A.2

Front

If the first term of an arithmetic sequence is 3 and the common difference is 4, what is the 10th term?

Back

The 10th term is \( a_{10} = 3 + (10-1)4 = 3 + 36 = 39 \).

Tags

CCSS.HSF.BF.A.2