Arithmetic and Geometric Sequences Flashcard

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

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

Back

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

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 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

Calculate the common ratio in the geometric sequence: 5, 10, 20, 40, 80.

Back

2

Front

Calculate the common ratio in the geometric sequence: 2, 6, 18, 54, 162.

Back

3

Front

Calculate the common difference in the arithmetic sequence: 4, 1, -2, -5, -8.

Back

-3

Front

Calculate the common difference in the arithmetic sequence: -6, -3, 0, 3, 6.

Back

3

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 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.