Intro to 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

Provide an example of an arithmetic sequence.

Back

An example of an arithmetic sequence is: 2, 5, 8, 11, 14 (common difference = 3).

Front

How do you find the common difference in a sequence?

Back

To find the common difference, subtract any term from the term that follows it (e.g., d = a2 - a1).

Front

True or False: The common difference can be negative in an arithmetic sequence.

Back

True.

Front

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

Back

The nth term (an) can be calculated using the formula: an = a1 + (n-1)d, where a1 is the first term and d is the common difference.

Front

If the first term of an arithmetic sequence is 4 and the common difference is 2, what is the 5th term?

Back

The 5th term is 4 + (5-1)2 = 4 + 8 = 12.

Front

True or False: An arithmetic sequence must always have a positive common difference.

Back

False.

Front

Is the sequence 10, 7, 4, 1 an arithmetic sequence?

Back

Yes, the common difference is -3.

Front

What is the common difference of the sequence: 20, 15, 10, 5?

Back

The common difference is -5.