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

How do you find the common difference in an arithmetic sequence?

Back

The common difference is found by subtracting any term from the subsequent term in the sequence.

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

What is a recursive rule in the context of arithmetic sequences?

Back

A recursive rule defines each term of the sequence based on the previous term(s). It typically includes the first term and a formula to find subsequent terms.

Front

Given the sequence 5, 12, 19, 26, what is the common difference?

Back

The common difference is 7.

Front

How do you write the recursive rule for the sequence 10, 20, 30, 40?

Back

a_1 = 10; a_n = a_{n-1} + 10.

Front

What are the next three terms in the sequence -33, -24, -15, -6?

Back

The next three terms are 3, 12, and 21.

Front

How do you find the 20th term of the sequence 5, 12, 19, 26?

Back

Use the formula a_n = a_1 + (n-1)d. Here, a_1 = 5, d = 7, so a_20 = 5 + (20-1)7 = 138.

Front

What is the first term of the sequence -49, -35, -21, -7?

Back

The first term (a_1) is -49.

Front

What is the common difference for the sequence 82, 76, 70, 64?

Back

The common difference is -6.