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.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers in which 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 determine if a sequence is arithmetic, geometric, or neither?

Back

To determine if a sequence is arithmetic, check if the difference between consecutive terms is constant. For geometric, check if the ratio of consecutive terms is constant. If neither condition is met, the sequence is neither.

Front

What is the formula for 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.

Front

What is the formula for 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.

Front

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

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The common difference in the sequence is 4.

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

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The common ratio in the sequence is 3.

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How can you find the 38th term of an arithmetic sequence?

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To find the 38th term of an arithmetic sequence, use the formula: a_n = a_1 + (n-1)d, substituting n with 38.

Front

What is the 38th term of the sequence 26, 22, 18, 14, ...?

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The 38th term of the sequence is -122.

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What is a sequence that is neither arithmetic nor geometric?

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A sequence is neither arithmetic nor geometric if it does not have a constant difference or a constant ratio between consecutive terms.