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

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?

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 a recursive formula for an arithmetic sequence?

Back

A recursive formula defines each term based on the previous term, typically written as: a_n = a_(n-1) + d.

Front

Given a_1 = 2 and d = 5, what are the first four terms of the sequence?

Back

2, 7, 12, 17.

Front

What is the explicit formula for the arithmetic sequence 5, 1, -3, -7?

Back

a_n = -4n + 9.

Front

How do you determine the common difference from a sequence?

Back

Subtract any term from the subsequent term; for example, in the sequence 5, 1, -3, -7, the common difference is 1 - 5 = -4.

Front

What is the 10th term of the sequence defined by a_1 = 8 and d = 2?

Back

The 10th term is a_10 = 8 + (10-1)2 = 8 + 18 = 26.

Front

What is the explicit formula for the sequence -10, -14, -18, -22?

Back

a_n = -4n - 6.

Front

If the 5th term of an arithmetic sequence is -10 and the common difference is -3, what is the 1st term?

Back

The 1st term is a_1 = -10 - 4(-3) = -10 + 12 = 2.