Arithmetic vs Geometric 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. This difference is called the common difference.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The nth term (a_n) of an arithmetic sequence 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.

Tags

CCSS.HSF.BF.A.2

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

What is the formula for the nth term of a geometric sequence?

Back

The nth term (a_n) of a geometric sequence can be calculated using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

In the sequence 9, 18, 27, 36, what is the common difference?

Back

The common difference is 9.

Tags

CCSS.HSF.BF.A.2

Front

In the geometric sequence -2, -4, -8, -16, what is the common ratio?

Back

The common ratio is 2.

Tags

CCSS.HSF.BF.A.2

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the distance from one term to the next in an arithmetic sequence.

Tags

CCSS.HSF.BF.A.2

Front

Identify if the sequence -34, -26, -18, -10, -2 is arithmetic, geometric, or neither.

Back

The sequence is arithmetic.

Tags

CCSS.HSF.BF.A.2

Front

What are the next three terms in the sequence 3, 7, 11, 15?

Back

The next three terms are 19, 23, 27.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

To find the common difference, subtract the first term from the second term (d = a_2 - a_1).

Tags

CCSS.HSF.BF.A.2