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 constant amount that each term in the sequence increases or decreases by.

Front

How do you find the common difference in a sequence?

Back

Subtract the first term from the second term (d = a2 - a1).

Front

Is the sequence 2, 4, 6, 8, ... arithmetic?

Back

Yes, the common difference is 2.

Front

Is the sequence 5, 10, 15, 20, ... arithmetic?

Back

Yes, the common difference is 5.

Front

Is the sequence 1, 2, 4, 8, ... arithmetic?

Back

No, the differences are not constant.

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.

Front

What is the 10th term of the sequence 3, 7, 11, ...?

Back

The 10th term is 39.

Front

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

Back

The sum S_n = n/2 * (a_1 + a_n) or S_n = n/2 * (2a_1 + (n-1)d).

Front

Find the 5th term of the sequence 4, 9, 14, ...

Back

The 5th term is 24.