Arithmetic Sequences - Introduction

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 constant amount that each term increases or decreases by in an arithmetic sequence.

Front

How do you determine if a sequence is arithmetic?

Back

To determine if a sequence is arithmetic, check if the difference between consecutive terms is the same.

Front

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

Back

The nth term (a_n) can be calculated 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 common difference of the sequence: 10, 15, 20, 25, ...

Back

d = 5

Front

Find the 10th term of the sequence: 2, 5, 8, 11, ...

Back

a_10 = 2 + (10-1)3 = 29

Front

Create the explicit formula for the sequence: 4, 7, 10, ...

Back

a_n = 3n + 1

Front

Is the sequence 12, 9, 6, 3, ... arithmetic?

Back

Yes, it is arithmetic with a common difference of -3.

Front

What is the 5th term of the sequence: 1, 4, 7, 10, ...?

Back

a_5 = 1 + (5-1)3 = 13

Front

If the first term of an arithmetic sequence is 5 and the common difference is 2, what is the 20th term?

Back

a_20 = 5 + (20-1)2 = 43