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 term that follows it.

Front

Given the sequence 5, 10, 15, 20, what is the common difference?

Back

The common difference is 5.

Front

What is the explicit formula for an arithmetic sequence?

Back

The explicit formula is a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference.

Front

What is the recursive formula for an arithmetic sequence?

Back

The recursive formula is a_n = a_(n-1) + d, where d is the common difference.

Front

If a_1 = 3 and d = 4, what is a_5?

Back

a_5 = 3 + (5 - 1) * 4 = 3 + 16 = 19.

Front

What is the 10th term of the sequence defined by a_n = 2n + 1?

Back

a_10 = 2(10) + 1 = 20 + 1 = 21.

Front

Is the sequence 2, 4, 8, 16 an arithmetic sequence?

Back

No, the sequence is not arithmetic because the difference between terms is not constant.

Front

What is the 64th term of the sequence defined by a_n = 5n + 4?

Back

a_64 = 5(64) + 4 = 320 + 4 = 324.

Front

How can you determine if a sequence is arithmetic?

Back

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