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 (d).

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The nth term of an arithmetic sequence 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.

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 (r).

Tags

CCSS.HSF.BF.A.2

Front

How do you find the nth term of a geometric sequence?

Back

The nth term of a geometric sequence can be found 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

What is the common difference in the arithmetic sequence 5, 8, 11, 14?

Back

The common difference (d) is 3, as each term increases by 3.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio in the geometric sequence 2, 6, 18, 54?

Back

The common ratio (r) is 3, as each term is multiplied by 3 to get the next term.

Tags

CCSS.HSF.BF.A.2

Front

Determine if the sequence 1, 4, 9, 16, ... is arithmetic or geometric.

Back

The sequence is neither arithmetic nor geometric; it is a sequence of perfect squares.

Tags

CCSS.HSF.BF.A.2

Front

What is the next term in the arithmetic sequence 10, 15, 20, ...?

Back

The next term is 25, as the common difference is 5.

Tags

CCSS.HSF.BF.A.2

Front

Identify the type of sequence: 3, 6, 12, 24, ...

Back

This is a geometric sequence with a common ratio of 2.

Tags

CCSS.HSF.BF.A.2

Front

What are the first five terms of the arithmetic sequence defined by f(n) = 2n + 3?

Back

The first five terms are 5, 7, 9, 11, 13.

Tags

CCSS.HSF.BF.A.2