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 (d) is found by subtracting any term from the subsequent term in the sequence.

Front

Given the sequence 3, 7, 11, 15, what is the common difference?

Back

The common difference is 4.

Front

What is the explicit formula for an arithmetic sequence?

Back

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

Front

If the first term of an arithmetic sequence is 5 and the common difference is 2, what is the 10th term?

Back

The 10th term is 5 + (10-1) * 2 = 23.

Front

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

Back

To find the nth term, use the formula a_n = a_1 + (n-1)d.

Front

What is the first term of the arithmetic sequence defined by the formula a_n = 2 + 3(n-1)?

Back

The first term (a_1) is 2.

Front

In the sequence 10, 7, 4, 1, what is the common difference?

Back

The common difference is -3.

Front

How can you determine the term before the first term in an arithmetic sequence?

Back

To find the term before the first term (term 0), use the formula a_0 = a_1 - d.

Front

What is the significance of the common difference in an arithmetic sequence?

Back

The common difference determines the rate at which the sequence increases or decreases.