Arithmetic Sequences and Their Properties

This video tutorial introduces arithmetic sequences, explaining their definition and formula. It covers the concept of a common difference and how to find the nth term using the arithmetic sequence formula. The tutorial includes example problems and solutions to help reinforce understanding, followed by practice problems for further learning.

What is an arithmetic sequence?

• A sequence where each term is the sum of the previous two terms.

• A sequence where each term is the square of the previous term.

• A sequence where each term is obtained by adding a constant to the previous term.

• A sequence where each term is a constant multiple of the previous term.

Which of the following is the general formula for the nth term of an arithmetic sequence?

• a_n = a_1 + (n - 1) * d

• a_n = a_1 * n + d

• a_n = a_1 + n * d

• a_n = a_1 * (n - 1) + d

What is the common difference in an arithmetic sequence?

• The sum of all terms in the sequence.

• The difference between any two consecutive terms.

• The difference between the first and last term.

• The product of the first and last term.

In the sequence 3, 7, 11, 15, what is the common difference?

• 4

• 3

• 2

• 5

How many differences are there between terms in a sequence of 100 terms?

• 100

• 99

• 101

• 98

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 4th term?

• 12

• 11

• 15

• 14

What is the nth term of the sequence 24, 32, 40, 48?

• 8n + 24

• 8n - 24

• 8n - 16

• 8n + 16

In the sequence -3, -10, -17, -24, what is the common difference?

• -4

• -6

• -7

• -5

What is the nth term of the sequence 5, 8, 11, 14?

• 3n - 5

• 3n + 5

• 3n + 2

• 3n - 2