Arithmetic and Geometric Sequences and Series Review

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 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.

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

How do you find the sum of a finite geometric series?

Back

The sum (S_n) of the first n terms of a geometric series can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), where a_1 is the first term and r is the common ratio.

Tags

CCSS.HSA.SSE.B.4

Front

What is the formula for the sum of an infinite geometric series?

Back

The sum (S) of an infinite geometric series can be calculated using the formula: S = a_1 / (1 - r), where |r| < 1.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference (d) is the constant amount that each term in an arithmetic sequence increases or decreases by.

Tags

CCSS.HSF.BF.A.2

Front

How do you find the common difference if given two terms of an arithmetic sequence?

Back

If a_n and a_m are two terms of an arithmetic sequence, the common difference can be found using the formula: d = (a_m - a_n) / (m - n).

Tags

CCSS.HSF.BF.A.2

Front

What is the first term of the sequence: 5, 8, 11, ...?

Back

The first term (a_1) of the sequence is 5.

Tags

CCSS.HSF.BF.A.2

Front

What is the 5th term of the arithmetic sequence: -8, -6, -4, -2...?

Back

The 5th term (a_5) is 2.

Tags

CCSS.HSF.BF.A.2