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

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

Back

The nth term 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 the first term of the sequence 5, 8, 11, ...?

Back

The first term (a_1) is 5.

Front

What is the common difference of the sequence 10, 20, 30, 40, ...?

Back

The common difference (d) is 10.

Front

Find the 22nd term of the sequence 5, 8, 11, ...

Back

The 22nd term is 68.

Front

What are the next two terms of the sequence 4, 7, 10, 13?

Back

The next two terms are 16 and 19.

Front

Write the recursive formula for the sequence 6, 4, 2, 0, ...

Back

The recursive formula is a_1 = 6, a_n = a_{n-1} - 2.

Front

What is the formula for the nth term of the sequence 12, 17, 22, 27?

Back

The nth term can be expressed as a_n = 12 + (n-1)5.

Front

How do you determine the next term in an arithmetic sequence?

Back

To find the next term, add the common difference to the last known term.