Sequences and Series Review

Front

What is a sequence?

Back

A sequence is an ordered list of numbers that follow a specific pattern or rule.

Front

What is a series?

Back

A series is the sum of the terms of a sequence.

Front

Define common difference in an arithmetic sequence.

Back

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

Front

How do you find the common difference if a2 = 6 and a6 = -14?

Back

The common difference (d) can be found using the formula: d = (a6 - a2) / (6 - 2) = (-14 - 6) / 4 = -5.

Front

What is the formula for the sum of the first n terms of an arithmetic series?

Back

The formula is S_n = n/2 * (a1 + an), where S_n is the sum, a1 is the first term, an is the nth term, and n is the number of terms.

Front

What is the formula for the sum of the first n terms of a geometric series?

Back

The formula is S_n = a1 * (1 - r^n) / (1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms.

Front

What is a finite geometric series?

Back

A finite geometric series is a series that has a limited number of terms and follows a geometric progression.

Front

What is an infinite geometric series?

Back

An infinite geometric series continues indefinitely and can converge to a finite value if the common ratio is between -1 and 1.

Front

Identify the type of series: 32 + 16 + 8 + 4 + 2 + 1.

Back

This is a finite geometric series with a common ratio of 1/2.

Front

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

Back

This is an arithmetic sequence with a common difference of 2. The 5th term (a5) is 0.