Algebra 2 Unit 1 Lesson 1-7 review

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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. This difference is called the common difference.

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How do you define a recursive sequence?

Back

A recursive sequence is defined by specifying the first term and a rule that relates each term to one or more previous terms.

Front

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

Back

The nth term of an arithmetic sequence 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.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

How do you define a recursive definition for a geometric sequence?

Back

A recursive definition for a geometric sequence specifies the first term and a rule that relates each term to the previous term using multiplication by the common ratio.

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What is the common difference in an arithmetic sequence?

Back

The common difference in an arithmetic sequence is the constant amount that each term increases or decreases by from the previous term.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio in a geometric sequence is the constant factor by which each term is multiplied to get the next term.

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If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 4th term?

Back

The 4th term is 5 + (4-1) * 3 = 5 + 9 = 14.

Front

If the first term of a geometric sequence is 2 and the common ratio is 3, what is the 3rd term?

Back

The 3rd term is 2 * 3^(3-1) = 2 * 9 = 18.

Front

What is the difference between arithmetic and geometric sequences?

Back

In arithmetic sequences, the difference between terms is constant (addition/subtraction), while in geometric sequences, the ratio between terms is constant (multiplication/division).