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 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 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 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

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

Back

The common difference (d) can be found by subtracting any term from the subsequent term: d = a_(n+1) - a_n.

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

Back

The common ratio (r) can be found by dividing any term by the previous term: r = a_(n+1) / a_n.

Front

What are the next two terms of the arithmetic sequence 13, 19, 25?

Back

The next two terms are 31 and 37.

Front

Which of the following is NOT an arithmetic sequence: -7, -13, -19, -25 or 3, 15, 75, 375?

Back

3, 15, 75, 375 is NOT an arithmetic sequence.

Front

What is the common difference of the sequence 2, -1, -4, -7?

Back

The common difference is -3.

Front

What is the first term of the arithmetic sequence defined by a_n = 5 + (n-1)2?

Back

The first term (a_1) is 5.