Exploring Arithmetic and Geometric Sequences and Series

The video tutorial explains the difference between sequences and series, focusing on arithmetic and geometric sequences. It covers how to find specific terms using formulas and recursive methods. The tutorial also discusses summing arithmetic and geometric series, including finite and infinite series. Advanced problems are solved to illustrate these concepts.

What is the main difference between a sequence and a series?

• A sequence is a list of terms, while a series is a sum of terms.

• A sequence uses multiplication, while a series uses addition.

• A sequence is always finite, while a series is always infinite.

• A sequence is a sum of terms, while a series is a list of terms.

In an arithmetic sequence, what is the common difference (D) if the sequence is 3, 5, 7, 9?

• 4

• 3

• 2

• 1

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

• a_n = a_1 + n * D

• a_n = a_1 * r^n

• a_n = a_1 * r^(n - 1)

• a_n = a_1 + (n - 1) * D

In a geometric sequence, what is the common ratio (r) if the sequence is 5, 15, 45, 135?

• 3

• 4

• 2

• 5

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

• a_n = a_1 + n * D

• a_n = a_1 * r^(n - 1)

• a_n = a_1 + (n - 1) * D

• a_n = a_1 * r^n

What is the sum of the first 10 terms of the geometric sequence 5, 15, 45, ...?

• 147620

• 147000

• 1476200

• 1470620

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

• S = a_1 * (1 + r)

• S = a_1 * (1 - r)

• S = a_1 / (1 + r)

• S = a_1 / (1 - r)

How many terms are there from 2 to 7 in a sequence?

• 4

• 5

• 6

• 7

What is the sum of the first 6 terms of the geometric sequence 1/2, 1/4, 1/8, ...?

• 63/64

• 64/63

• 32/31

• 31/32

What is the sum of the infinite geometric series 100, 50, 25, ...?

• 150

• 300

• 200

• 250