Geometric Sequences and Their Properties

The video tutorial covers geometric sequences, focusing on the concept of the common ratio and how it is used to generate terms in a sequence. It explains the explicit and recursive rules for geometric sequences, providing examples and calculations. The tutorial also demonstrates solving for unknowns in sequences and using calculators to verify results.

What is the common ratio in a geometric sequence?

• The difference between consecutive terms

• The ratio of a term to its previous term

• The sum of consecutive terms

• The product of consecutive terms

In the formula for the nth term of a geometric sequence, what does 'a sub 1' represent?

• The first term

• The common ratio

• The nth term

• The previous term

If a sequence is geometric and the first term is 4 and the common ratio is 3, what is the third term?

• 12

• 36

• 108

• 27

How do you determine if a sequence is geometric?

• By checking if the terms are divided by a constant

• By checking if the terms are multiplied by a constant

• By checking if the terms are added by a constant

• By checking if the terms are subtracted by a constant

Given a geometric sequence with a sub 2 = 15 and a sub 5 = 405, what is the common ratio?

• 4

• 3

• 5

• 2

What is the explicit rule for a geometric sequence with a sub 1 = 5 and r = 2?

• a sub n = 5 * 2^n

• a sub n = 5 * 2^(n-1)

• a sub n = 5 + 2^n

• a sub n = 5 + 2^(n-1)

How do you find the 7th term in a geometric sequence with a sub 1 = 2 and r = -4?

• 2 * (-4)^4

• 2 * (-4)^7

• 2 * (-4)^5

• 2 * (-4)^6

What is the recursive rule for a geometric sequence with a sub 1 = 4 and r = 3?

• a sub n = 4 * 3^(n-1)

• a sub n = a sub (n-1) * 3

• a sub n = 4 + 3^(n-1)

• a sub n = a sub (n-1) + 3

If a geometric sequence has a sub 1 = 5 and r = 1/2, what is the 10th term?

• 5/512

• 5/1024

• 5/256

• 5/128

What is the advantage of using the explicit rule over the recursive rule in geometric sequences?

• It requires less calculation

• It is more accurate

• It allows finding any term without knowing the previous terms

• It is easier to understand