Arithmetic Sequences - Introduction

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 constant amount that each term increases or decreases by in an arithmetic sequence.

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CCSS.HSF.BF.A.2

Front

How do you determine if a sequence is arithmetic?

Back

To determine if a sequence is arithmetic, check if the difference between consecutive terms is the same.

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CCSS.HSF.BF.A.2

Front

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

Back

The nth term (a_n) can be calculated using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

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CCSS.HSF.BF.A.2

Front

Find the common difference of the sequence: 10, 15, 20, 25, ...

Back

d = 5

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CCSS.HSF.BF.A.2

Front

Find the 10th term of the sequence: 2, 5, 8, 11, ...

Back

a_10 = 2 + (10-1)3 = 29

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CCSS.HSF.BF.A.2

Front

Create the explicit formula for the sequence: 4, 7, 10, ...

Back

a_n = 3n + 1

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CCSS.HSF.BF.A.2

Front

Is the sequence 12, 9, 6, 3, ... arithmetic?

Back

Yes, it is arithmetic with a common difference of -3.

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CCSS.HSF.BF.A.2

Front

What is the 5th term of the sequence: 1, 4, 7, 10, ...?

Back

a_5 = 1 + (5-1)3 = 13

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CCSS.HSF.BF.A.2

Front

If the first term of an arithmetic sequence is 5 and the common difference is 2, what is the 20th term?

Back

a_20 = 5 + (20-1)2 = 43

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CCSS.HSF.BF.A.2