Arithmetic and Geometric 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. This difference is called the common difference.

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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.

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CCSS.HSF.BF.A.2

Front

How do you find 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.

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CCSS.HSF.BF.A.2

Front

How do you 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), where a_1 is the first term and r is the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

What is the common difference in the sequence 3, 7, 11, 15?

Back

The common difference is 4, as each term increases by 4.

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CCSS.HSF.BF.A.2

Front

What is the common ratio in the sequence 2, 6, 18, 54?

Back

The common ratio is 3, as each term is multiplied by 3 to get the next term.

Tags

CCSS.HSF.BF.A.2

Front

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term?

Back

The 10th term is 32.

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CCSS.HSF.BF.A.2

Front

If the first term of a geometric sequence is 4 and the common ratio is 2, what is the 5th term?

Back

The 5th term is 64.

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CCSS.HSF.BF.A.2

Front

What is the sum of the first n terms of an arithmetic sequence?

Back

The sum can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where S_n is the sum of the first n terms, a_1 is the first term, and a_n is the nth term.

Front

What is the sum of the first n terms of a geometric sequence?

Back

The sum can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), where S_n is the sum of the first n terms, a_1 is the first term, and r is the common ratio.

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CCSS.HSA.SSE.B.4