Finding Values in Exponential Sequences

The video tutorial explains a sequence where each term is derived by multiplying the previous term by four, starting with an initial value of three. The teacher demonstrates how to derive an explicit rule for the sequence, which allows finding any term by using the formula a_sub_n = 3 * 4^(n-1). The explanation includes understanding the multiplication pattern and how the number of multiplications relates to the term's position in the sequence.

What is the first value in the sequence?

• 3

• 2

• 4

• 1

How is the second value in the sequence determined?

• By dividing the first value by 2

• By subtracting 1 from the first value

• By adding 4 to the first value

• By multiplying the first value by 4

What operation is repeatedly used to find the next value in the sequence?

• Division

• Multiplication

• Subtraction

• Addition

What is the starting value needed to write an explicit rule for the sequence?

• 3

• 4

• 2

• 1

How many times do you multiply by four to find the third value in the sequence?

• Three times

• Four times

• Once

• Twice

For the fourth value in the sequence, how many times is the previous value multiplied by four?

• Three times

• Four times

• Once

• Twice

What is the general formula for finding any value in the sequence?

• a_n = 3 * 4^(n-2)

• a_n = 3 * 4^(n+1)

• a_n = 3 * 4^(n-1)

• a_n = 3 * 4^n

In the explicit rule, what does the exponent in 4^(n-1) represent?

• The position in the sequence

• The final value

• The number of times to multiply by four

• The starting value

Why is the exponent in the formula one less than the position in the sequence?

• Because the sequence starts at zero

• Because the first value is not multiplied

• Because the sequence is decreasing

• Because the sequence is non-linear