Arithmetic Sequences

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 common difference in an arithmetic sequence.

Back

The common difference is the constant amount that each term in an arithmetic sequence increases or decreases by.

Front

Identify the common difference: 10, 20, 30, 40, ...

Back

10

Front

Given the recursive rule, find the 7th term of the arithmetic sequence: a_n = a_(n-1) + d, where a_1 = 2 and d = 2.

Back

10.4

Front

Find the common difference: 29, 21, 13, 5, ...

Back

d = -8

Front

What are the next two terms of the sequence 4, 7, 10, 13?

Back

16 and 19

Front

Find the common difference: 1, 201, 401, 601, ...

Back

d = 200

Front

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

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 formula for the sum of the first n terms of an arithmetic sequence?

Back

The sum S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 5th term?

Back

The 5th term is 5 + (5-1) * 3 = 17.