Arithmetic Sequences: Explicit & Recursive Formulas

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 using the explicit formula?

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 recursive formula for an arithmetic sequence?

Back

The recursive formula is: a_n = a_(n-1) + d, where d is the common difference.

Front

Given the sequence 2, -1, -4, -7,..., what is the common difference?

Back

-3

Front

Using the recursive formula a_n = a_(n-1) + 5, with a_1 = -16, what are the first four terms?

Back

-16, -11, -6, -1

Front

How do you determine if a sequence is arithmetic?

Back

A sequence is arithmetic if the difference between any two consecutive terms is the same.

Front

What is the explicit formula for the arithmetic sequence -15, -35, -55, -75,...?

Back

a_n = -15 - 20(n-1) or a_n = -15 - 20n + 20.

Front

Find the 26th term of the sequence -15, -35, -55, -75,...

Back

-515

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.