Arithmetic Sequence (Recursive and Explicit)

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

Define the common difference in an arithmetic sequence.

Back

The common difference (d) is the constant amount that each term in the sequence increases or decreases by.

Front

How do you find the common difference in the sequence: -34, -29, -24, -19, ...?

Back

d = -29 - (-34) = 5.

Front

What are the next three terms in the arithmetic sequence: 25, 34, 43, 52, ...?

Back

The next three terms are 61, 70, 79.

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

Find the 32nd term of the sequence: 9, 4, -1, -6, -11, ...

Back

The 32nd term is -146.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

a_n = a_1 + (n-1)d.

Front

How do you determine the common difference in the sequence: 29, 21, 13, 5, ...?

Back

d = 21 - 29 = -8.

Front

What are the next three terms in the arithmetic sequence: -33, -24, -15, -6, ...?

Back

The next three terms are 3, 12, 21.

Front

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

Back

The 10th term is 10 + (10-1)3 = 37.