Understanding Geometric Sequences

The video tutorial explains a sequence defined by F(n) = 1/5 * F(n-1) with the first term F(1) = 50. It guides viewers to calculate and graph the sequence for n = 1 to 4, illustrating exponential decay. The sequence is defined recursively, and the video contrasts geometric and arithmetic sequences, highlighting their graphical differences.

What is the initial term of the sequence defined in the video?

• 10

• 20

• 50

• 100

How is the value of F(2) calculated in the sequence?

• F(1) - 5

• F(1) + 5

• 5 * F(1)

• 1/5 * F(1)

What is the value of F(3) in the sequence?

• 5

• 10

• 1

• 2

What pattern is observed in the graph of the sequence?

• Linear growth

• Exponential decay

• Constant value

• Exponential growth

How is a geometric sequence defined in the video?

• Each term is the sum of the previous term and a constant

• Each term is a multiple of the previous term

• Each term is the difference of the previous term and a constant

• Each term is a division of the previous term

What is the recursive nature of the sequence discussed?

• Each term is independent of the previous term

• Each term is the sum of all previous terms

• Each term is defined in terms of the previous term

• Each term is a fixed value

What is a key difference between geometric and arithmetic sequences?

• Arithmetic sequences have exponential growth

• Geometric sequences have constant differences

• Arithmetic sequences have constant ratios

• Geometric sequences have constant ratios

What happens to the terms in a geometric sequence with a multiplier less than one?

• They oscillate

• They increase

• They decrease

• They remain constant

What type of curve do points in a geometric sequence with a multiplier less than one form?

• Circular

• Linear

• Parabolic

• Exponential

In an arithmetic sequence, how is each successive term determined?

• By dividing the previous term

• By multiplying the previous term

• By taking the square root of the previous term

• By adding or subtracting a fixed amount