Lesson 4-7 Review Arithmetic Sequences. Recursive/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 explicit formula for an arithmetic sequence.

Back

The explicit formula for an arithmetic sequence is given by: a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference.

Front

What is the recursive formula for an arithmetic sequence?

Back

The recursive formula for an arithmetic sequence is given by: a_1 = first term; a_n = a_{n-1} + d, where d is the common difference.

Front

Find the first four terms of the sequence defined by a_1 = 5; a_n = a_{n-1} + 3.

Back

The first four terms are: 5, 8, 11, 14.

Front

What is the common difference in the sequence: 2, 5, 8, 11, ...?

Back

The common difference is 3.

Front

How do you find the nth term of an arithmetic sequence?

Back

To find the nth term, use the explicit formula: a_n = a_1 + (n - 1)d.

Front

Given the sequence: 10, 7, 4, 1, ... what is the common difference?

Back

The common difference is -3.

Front

Write the explicit formula for the sequence: 4, 10, 16, 22, ...

Back

The explicit formula is a_n = 4 + 6(n - 1).

Front

Identify the recursive rule for the sequence: 15, 12, 9, 6, ...

Back

The recursive rule is: a_1 = 15; a_n = a_{n-1} - 3.

Front

What is the first term of the sequence defined by a_n = 2n + 1?

Back

The first term (a_1) is 3.