Inductive Reasoning: Sequences and Series

The video tutorial explains how to find the nth term in a sequence where each term increases by 3, starting from 6. The instructor identifies the pattern and derives a general expression for the nth term as 3(n + 1) or 3n + 3. The expression is verified for different terms to ensure its accuracy.

What is the first term in the given sequence?

• 12

• 3

• 6

• 9

What is the second term in the sequence?

• 12

• 6

• 15

• 9

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

• 4

• 5

• 3

• 2

What is the third term in the sequence?

• 18

• 15

• 12

• 9

How do you express the first term as a multiple of 3?

• 3 x 3

• 3 x 4

• 3 x 2

• 3 x 1

What is the general expression for the nth term in the sequence?

• 3n

• 3(n+1)

• 3(n-1)

• 3n+3

What is the value of the 4th term in the sequence?

• 21

• 18

• 15

• 12

If n=5, what is the value of the nth term using the formula 3(n+1)?

• 21

• 18

• 24

• 15

What is the value of the nth term if n=1 using the formula 3n+3?

• 12

• 9

• 6

• 3

What is the value of the nth term if n=2 using the formula 3n+3?

• 15

• 9

• 6

• 12