6.17 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

How do you find the common difference in an arithmetic sequence?

Back

The common difference is found by subtracting any term from the subsequent term in the sequence.

Front

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

Back

The nth term (a_n) of an arithmetic sequence can be calculated using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term?

Back

The 10th term is 32, calculated as: a_10 = 5 + (10-1)3 = 5 + 27 = 32.

Front

What is the term used to describe each individual number in a sequence?

Back

Each individual number in a sequence is called a 'term'.

Front

Given the sequence 2, 5, 8, 11, what is the common difference?

Back

The common difference is 3.

Front

What are the next three terms in the sequence 4, 9, 14, 19?

Back

The next three terms are 24, 29, and 34.

Front

How can you determine if a sequence is arithmetic?

Back

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

Front

What is the common difference in the sequence 15, 25, 35, 45?

Back

The common difference is 10.

Front

If an arithmetic sequence has a common difference of -2, what is the next term after 10?

Back

The next term is 8, calculated as: 10 + (-2) = 8.