Arithmetic and Geometric Sequences

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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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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

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

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The nth term of an arithmetic sequence can be found using the formula: \( a_n = a_1 + (n-1)d \) where \( a_1 \) is the first term and \( d \) is the common difference.

Front

What is the formula for the nth term of a geometric sequence?

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The nth term of a geometric sequence can be found using the formula: \( a_n = a_1 \cdot r^{(n-1)} \) where \( a_1 \) is the first term and \( r \) is the common ratio.

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

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The common difference \( d \) can be found by subtracting any term from the term that follows it: \( d = a_{n+1} - a_n \).

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

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The common ratio \( r \) can be found by dividing any term by the term that precedes it: \( r = \frac{a_{n+1}}{a_n} \).

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What is the 5th term of the arithmetic sequence: 2, 5, 8, 11, ...?

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The 5th term is 14.

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What is the 4th term of the geometric sequence: 3, 6, 12, 24, ...?

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The 4th term is 24.

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What is the common difference of the arithmetic sequence: 10, 15, 20, 25, ...?

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The common difference is 5.

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What is the common ratio of the geometric sequence: 5, 10, 20, 40, ...?

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The common ratio is 2.