Arithmetic and 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 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 an arithmetic sequence?

Back

The formula is a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the term number.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The formula is a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The common difference (d) is found by subtracting any term from the subsequent term: d = a_(n+1) - a_n.

Tags

CCSS.HSF.BF.A.2

Front

How do you find the common ratio in a geometric sequence?

Back

The common ratio (r) is found by dividing any term by the previous term: r = a_(n+1) / a_n.

Tags

CCSS.HSF.BF.A.2

Front

What is the next term in the arithmetic sequence 3, 7, 11, 15?

Back

The next term is 19.

Tags

CCSS.HSF.BF.A.2

Front

What is the next term in the geometric sequence 2, 6, 18, 54?

Back

The next term is 162.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The 10th term is 32.

Tags

CCSS.HSF.BF.A.2

Front

If the first term of a geometric sequence is 4 and the common ratio is 2, what is the 6th term?

Back

The 6th term is 128.

Tags

CCSS.HSF.BF.A.2