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 formula is 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 formula is 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 subsequent term: d = a_(n+1) - a_n.

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 previous term: r = a_n / a_(n-1).

Front

What is the first term of the sequence 11, 22, 44, 88...?

Back

The first term (a_1) is 11.

Front

What is the common ratio of the sequence 2, 8, 32, 128...?

Back

The common ratio (r) is 4.

Front

If a geometric sequence starts with 2 and has a common ratio of 5, what is the 4th term?

Back

The 4th term is 2 * 5^(4-1) = 250.

Front

What is the 7th term of the sequence 2, 10, 50...?

Back

The 7th term is 2 * 5^(7-1) = 31,250.