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.' For example, in the sequence 2, 4, 6, 8, the common difference is 2.

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, d is the common difference, and n is the term number.

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.' For example, in the sequence 3, 6, 12, 24, the common ratio is 2.

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, r is the common ratio, and n is the term number.

Front

What is the common difference in the arithmetic sequence 5, 10, 15, 20?

Back

The common difference is 5, as each term increases by 5.

Front

What is the common ratio in the geometric sequence 2, 6, 18, 54?

Back

The common ratio is 3, as each term is multiplied by 3 to get the next term.

Front

Find the next term in the arithmetic sequence 4, 8, 12, 16.

Back

The next term is 20.

Front

Find the next term in the geometric sequence 5, 15, 45, 135.

Back

The next term is 405.

Front

What is the first term of the arithmetic sequence if the second term is 10 and the common difference is 2?

Back

The first term is 8.

Front

What is the first term of the geometric sequence if the second term is 12 and the common ratio is 3?

Back

The first term is 4.