Geometric and Arithmetic Sequences

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 an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference.

Front

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

Back

To find the common ratio, divide any term by the previous term (r = a_n / a_(n-1)).

Front

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

Back

To find the common difference, subtract any term from the previous term (d = a_n - a_(n-1)).

Front

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

Back

The nth term (a_n) 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 (a_n) 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 ratio for the sequence: 28, 14, 7, 3.5...?

Back

1/2

Front

Find the 22nd term of the sequence: 5, 8, 11,...

Back

68

Front

What is the common ratio of the geometric sequence -1, 6, -36, 216...?

Back

-6

Front

What is the common ratio of the sequence 5, 25, 125...?

Back

5