Practice Explicit & Recursive Sequences

Front

What is a recursive sequence?

Back

A recursive sequence is a sequence in which each term is defined as a function of one or more of the preceding terms.

Front

What is an explicit formula?

Back

An explicit formula defines the nth term of a sequence directly in terms of n, without referring to previous terms.

Front

Write the recursive formula for the sequence 6, 17, 28, 39, 50.

Back

a_n = a_{n-1} + 11, a_1 = 6.

Front

What are the next two terms of the arithmetic sequence 13, 19, 25?

Back

31 and 37.

Front

What is the common difference in the sequence 2, -1, -4, -7?

Back

-3.

Front

Identify the explicit formula for the arithmetic sequence 2, 9, 16, 23.

Back

a_n = 7n - 5.

Front

Which sequence 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

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

Back

a_n = a_1 + (n-1)d, where d is the common difference.

Front

How do you find the common difference in an arithmetic sequence?

Back

Subtract the first term from the second term (d = a_2 - a_1).

Front

What is the first term of the sequence defined by a_n = 5n - 2?

Back

The first term is a_1 = 5(1) - 2 = 3.