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 fixed amount added to each term to get the next term in the sequence.

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, where a_1 is the first term and d is the common difference.

Front

What is the explicit formula for the arithmetic sequence 6, 11, 16, 21?

Back

a_n = 6 + 5(n - 1) where n is the term number.

Front

Which of the following is NOT an arithmetic sequence: -7, -13, -19, -25 or 3, 15, 75, 375?

Back

3, 15, 75, 375 is NOT an arithmetic sequence.

Front

Is the sequence 78, 785, 7855, 78555 arithmetic?

Back

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

Front

Write the explicit equation for the sequence 25, 21, 17, 13.

Back

a_n = 25 - 4(n - 1).

Front

What are the next two terms in the sequence 4, 7, 10, 13?

Back

The next two terms are 16 and 19.

Front

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

Back

The 5th term is 10 + 4(3) = 22.

Front

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

Back

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