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 the formula for the nth term of an arithmetic sequence?

Back

The nth term (a_n) can be calculated 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 (a_n) can be calculated 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) is found by subtracting any term from the term that follows it: d = a_n - a_(n-1).

Front

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

Back

The common ratio (r) is found by dividing any term by the term that precedes it: r = a_n / a_(n-1).

Front

What is the next term in the arithmetic sequence 3, 7, 11, 15?

Back

The next term is 19.

Front

What is the next term in the geometric sequence 2, 6, 18, 54?

Back

The next term is 162.

Front

What is the common difference in the sequence 10, 7, 4, 1?

Back

The common difference is -3.

Front

What is the common ratio in the sequence 1, 3, 9, 27?

Back

The common ratio is 3.