Algebra 2 Midterm

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What is an arithmetic sequence?

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An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference (d).

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CCSS.HSF.BF.A.2

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How do you find the common difference in an arithmetic sequence?

Back

To find the common difference (d) in an arithmetic sequence, subtract any term from the subsequent term: d = a_{n+1} - a_n.

Tags

CCSS.HSF.BF.A.2

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 (r).

Tags

CCSS.HSF.BF.A.2

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How do you find the common ratio in a geometric sequence?

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To find the common ratio (r) in a geometric sequence, divide any term by the previous term: r = a_{n+1} / a_n.

Tags

CCSS.HSF.BF.A.2

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What is the explicit formula for an arithmetic sequence?

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The explicit formula for an arithmetic sequence is given by: 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

Front

What is the explicit formula for a geometric sequence?

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The explicit formula for a geometric sequence is given by: a_n = a_1 * r^{(n-1)}, where a_1 is the first term and r is the common ratio.

Tags

CCSS.HSF.BF.A.2

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How do you determine if a sequence is arithmetic or geometric?

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To determine if a sequence is arithmetic, check if the difference between consecutive terms is constant. To determine if it is geometric, check if the ratio of consecutive terms is constant.

Tags

CCSS.HSF.BF.A.2

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What is the formula to find the nth term of an arithmetic sequence?

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The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n-1)d.

Tags

CCSS.HSF.BF.A.2

Front

What is the formula to find the nth term of a geometric sequence?

Back

The nth term of a geometric sequence can be found using the formula: a_n = a_1 * r^{(n-1)}.

Tags

CCSS.HSF.BF.A.2

Front

How do you find the 20th term of an arithmetic sequence given the formula a_n = 45 + 3(n-1)?

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To find a_{20}, substitute n = 20 into the formula: a_{20} = 45 + 3(20-1) = 102.

Tags

CCSS.HSF.BF.A.2