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.

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

What is the common difference in an arithmetic sequence?

Back

The common difference is the amount added to each term to get the next term in an arithmetic sequence.

Front

What is the common ratio in a geometric sequence?

Back

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

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.

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.

Front

What is the first term of the sequence 5, 10, 15, 20...?

Back

The first term is 5.

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What is the 5th term of the arithmetic sequence 2, 4, 6, 8...?

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The 5th term is 10.

Front

What is the 3rd term of the geometric sequence 2, 6, 18, 54...?

Back

The 3rd term is 18.

Front

If the common difference is 3, what is the 10th term of the sequence 1, 4, 7, ...?

Back

The 10th term is 28.