Arithmetic and Geometric Sequences with Word Problems

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 common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in the sequence.

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 common ratio in a geometric sequence?

Back

The common ratio is the factor by which we multiply each term to get the next term in the sequence.

Front

How do you determine if a sequence is arithmetic?

Back

A sequence is arithmetic if the difference between consecutive terms is the same.

Front

How do you determine if a sequence is geometric?

Back

A sequence is geometric if the ratio of consecutive terms is the same.

Front

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 4th term?

Back

The 4th term is 5 + 3(4-1) = 14.

Front

If the first term of a geometric sequence is 2 and the common ratio is 3, what is the 3rd term?

Back

The 3rd term is 2 * 3^(3-1) = 18.

Front

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

Back

The nth term is given by 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 is given by a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.