Recursive & Explicit Arithmetic Sequences

Front

What is a recursive arithmetic sequence?

Back

A recursive arithmetic sequence is defined by a starting term and a rule that relates each term to the previous term, typically in the form a_n = a_(n-1) + d, where d is the common difference.

Front

What is an explicit arithmetic sequence?

Back

An explicit arithmetic sequence is defined by a formula that allows you to calculate the nth term directly, typically in the form a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

Identify the first four terms of the recursive sequence: a_1 = 10; a_n = a_(n-1) + 5.

Back

10, 15, 20, 25

Front

Identify the first four terms of the recursive sequence: a_1 = 50; a_n = a_(n-1) - 3.

Back

50, 47, 44, 41

Front

How do you determine if a sequence is arithmetic?

Back

A sequence is arithmetic if the difference between consecutive terms is constant.

Front

What is the common difference in the sequence: 4, 8, 12, 16, ...?

Back

The common difference is 4.

Front

Write the recursive rule for the arithmetic sequence: 30, 25, 20, 15, ...

Back

a_1 = 30; a_n = a_(n-1) - 5.

Front

Write the explicit rule for the arithmetic sequence: 7, 10, 13, 16, ...

Back

a_n = 7 + 3(n-1).

Front

Identify the first four terms of the recursive sequence: a_1 = 100; a_n = a_(n-1) + 10.

Back

100, 110, 120, 130

Front

What is the explicit formula for the sequence: 2, 5, 8, 11, ...?

Back

a_n = 2 + 3(n-1).