Arithmetic Sequences and Their Properties

The video tutorial explains how to determine which term in an arithmetic sequence equals 153. It begins by identifying the first term and the common difference of the sequence. The tutorial then demonstrates how to use the arithmetic sequence formula to set up an equation. By solving this equation, the tutorial finds that the 39th term of the sequence is 153. The process involves understanding the sequence, calculating the common difference, and solving the equation step-by-step.

What is the main problem discussed in the video?

• Calculating the average of the sequence

• Determining which term in the sequence is 153

• Identifying the 153rd term in a sequence

• Finding the sum of an arithmetic sequence

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

• a_n = a_1 / n + d

• a_n = a_1 * n + d

• a_n = a_1 + (n - 1) * d

• a_n = a_1 - (n - 1) * d

What is the first term (a_1) of the sequence given in the video?

• 13

• 5

• 1

• 9

How is the common difference (d) calculated in an arithmetic sequence?

• By adding the first and last terms

• By subtracting any term from the previous term

• By dividing the last term by the first term

• By multiplying the first term by the number of terms

What is the common difference (d) in the sequence 1, 5, 9, 13?

• 5

• 4

• 3

• 2

What value is substituted for a_n in the formula to find the term number?

• 4

• 39

• 153

• 1

What is the next step after substituting known values into the formula?

• Divide by the common difference

• Clear the parentheses by distributing

• Multiply all terms

• Add all terms together

What operation is performed to isolate 4n in the equation?

• Multiply both sides by 4

• Subtract 3 from both sides

• Divide both sides by 4

• Add 3 to both sides

What is the value of n when the equation is solved?

• 153

• 4

• 39

• 156

Which term in the sequence is 153?

• 39th

• 153rd

• 1st

• 4th