Arithmetic Sequences: Identifying, Writing Equations, and Finding Terms

The video tutorial covers arithmetic sequences, explaining how to identify terms and write them as functions. It discusses the concept of common difference, graphing sequences, and formulating equations. The tutorial includes practice problems to reinforce learning.

What is an arithmetic sequence?

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

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

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

• A sequence where the sum of terms is constant.

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

• 2

• 3

• 4

• 5

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

• 15

• 13

• 11

• 9

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

• Quadratic

• Logarithmic

• Exponential

• Linear

Why is an arithmetic sequence considered a discrete function?

• Because it has a continuous range of values.

• Because it only includes whole number terms.

• Because it can have fractional terms.

• Because it is not defined for negative numbers.

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

• a_n = a_1 / (n-1)d

• a_n = a_1 - (n-1)d

• a_n = a_1 * d^(n-1)

• a_n = a_1 + (n-1)d

If the first term is 10 and the common difference is -2, what is the 5th term?

• 6

• 4

• 2

• 0

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 + 34*(-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)

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

• 152

• 150

• 154

• 148

Which of the following is NOT a characteristic of an arithmetic sequence?

• It has a constant common difference.

• It is a discrete function.

• It can be represented as a linear function.

• It has a variable common difference.