Arithmetic 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 common difference in an arithmetic sequence?

Back

The common difference is the fixed amount that each term increases or decreases by in an arithmetic sequence.

Front

Is the sequence 5, 4.25, 3.5, 2.75 an arithmetic sequence?

Back

Yes, because the difference between each term is constant (-0.75).

Front

What is the explicit formula for the arithmetic sequence 2, 8, 14, ...?

Back

a_n = 6n - 4.

Front

How do you find the nth term of an arithmetic sequence?

Back

Use 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 the 22nd term of the sequence 5, 8, 11, ...?

Back

68.

Front

What is the recursive formula for the sequence 6, 4, 2, 0, ...?

Back

a_n = a_{n-1} - 2, with a_1 = 6.

Front

How do you identify the common difference in a sequence?

Back

Subtract the first term from the second term (or any two consecutive terms).

Front

What is the first term of the arithmetic sequence defined by a_n = 3n + 2?

Back

The first term (a_1) is 5.

Front

If the common difference is 4, what is the 5th term of the sequence starting with 2?

Back

The 5th term is 18.