Arithmetic sequence

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 constant amount that is added to each term to get the next term in the sequence.

Front

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

Back

3

Front

If the first term of an arithmetic sequence is 4 and the common difference is 3, what is the 5th term?

Back

The 5th term is 4 + (5-1) * 3 = 16.

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

Find the 10th term of the arithmetic sequence defined by a_n = 3 + 2(n-1).

Back

The 10th term is a_10 = 3 + 2(10-1) = 21.

Front

What is the 22nd term of the sequence defined by a_n = 5 - 3n?

Back

a_22 = 5 - 3(22) = -61.

Front

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

Back

Use the formula a_n = a_1 + (n-1)d.

Front

What is the sum of the first n terms of an arithmetic sequence?

Back

The sum S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

If the first term is 10 and the common difference is -2, what is the 6th term?

Back

The 6th term is 10 + (6-1)(-2) = 0.