Understanding Arithmetic Sequences

The video tutorial introduces arithmetic sequences, explaining how to identify terms and write them as functions. It covers the concept of common difference, demonstrates how to find subsequent terms, and explains graphing sequences as linear functions. The tutorial also guides viewers on writing equations for sequences and finding specific terms using these equations. The session concludes with practice exercises to reinforce learning.

What is an arithmetic sequence?

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

• A sequence where the sum of consecutive terms is constant.

• A sequence where the difference between consecutive terms is constant.

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

In the sequence 3, 6, 9, 12, what is the common difference?

• 5

• 2

• 3

• 4

If the first term of an arithmetic sequence is 5 and the common difference is 2, what is the third term?

• 7

• 9

• 11

• 13

What type of function does an arithmetic sequence represent when graphed?

• Logarithmic

• Linear

• Quadratic

• Exponential

Why is an arithmetic sequence considered a discrete function?

• Because it has no common difference.

• Because it is continuous.

• Because it can have fractional terms.

• Because it includes only integer values.

What is the formula for the nth term of an arithmetic sequence?

• a_n = a_1 + (n-1)d

• a_n = a_1 * d^(n-1)

• a_n = a_1 - (n-1)d

• a_n = a_1 / (n-1)d

If the first term is 10 and the common difference is 4, what is the 5th term?

• 30

• 18

• 22

• 26

How do you find the 35th term of an arithmetic sequence with a first term of 16 and a common difference of -4?

• Use the formula a_n = 16 + 35*(-4)

• Use the formula a_n = 16 - 34*(-4)

• Use the formula a_n = 16 - 35*(-4)

• Use the formula a_n = 16 + 34*(-4)

What is the 45th term of an arithmetic sequence with a first term of -6 and a common difference of 3.5?

• 150

• 152

• 154

• 148

Why is it important to learn the formula for arithmetic sequences?

• To easily find large terms without listing all previous terms.

• To calculate the sum of all terms.

• To solve quadratic equations.

• To understand geometric sequences.