Arithmetic Sequences and Explicit Rules

The video tutorial explains how to identify the explicit rule for a given sequence. It starts by introducing a sequence of numbers and labeling them. The pattern of adding two to each number is identified, and different sequence rules are evaluated to find the correct one. The tutorial concludes by verifying the correct rule through calculation.

What are the first four terms of the sequence discussed in the video?

• 5, 7, 9, 11

• 6, 8, 10, 12

• 7, 9, 11, 13

• 4, 6, 8, 10

What is the common difference between consecutive terms in the sequence?

• 4

• 3

• 2

• 1

Which explicit rule does not work for the sequence because it starts with the wrong initial value?

• a_n = 7 + 2(n-1)

• a_n = 6 + 3(n-1)

• a_n = 8 + 3(n-1)

• a_n = 5 + 2(n-1)

Why do the explicit rules C and D not work for the sequence?

• They start with the wrong initial value.

• They are not arithmetic sequences.

• They have the wrong number of terms.

• They have the wrong common difference.

What is the correct explicit rule for the sequence?

• a_n = 7 + 2(n-1)

• a_n = 5 + 2(n-1)

• a_n = 8 + 3(n-1)

• a_n = 6 + 3(n-1)

How can you verify the correctness of the explicit rule for a specific term?

• By checking if the term matches the sequence.

• By comparing it with another sequence.

• By using a different rule.

• By changing the common difference.

What is the value of the third term in the sequence using the correct explicit rule?

• 11

• 9

• 7

• 5