Understanding Geometric Sequences

The video tutorial explains geometric sequences, focusing on the concept of multiplying by a constant ratio to find subsequent terms. It introduces the formula a_n = a_1 * r^(n-1) and demonstrates how to find terms using both recursive and explicit methods. The tutorial also covers solving for unknowns in a sequence when given specific terms, using a system of equations. The video highlights the exponential nature of geometric sequences compared to arithmetic sequences.

What is the defining characteristic of a geometric sequence?

• Dividing by the same ratio to get the next term

• Adding a constant number to each term

• Subtracting a constant number from each term

• Multiplying by the same ratio to get the next term

In the formula a_n = a_1 * r^(n-1), what does 'r' represent?

• The first term of the sequence

• The number of terms in the sequence

• The common ratio of the sequence

• The last term of the sequence

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 5th term?

• 96

• 24

• 48

• 12

How is the common ratio in a geometric sequence determined?

• By subtracting the first term from the last term

• By dividing a term by its previous term

• By multiplying the first term by the last term

• By adding the first and last terms

What is the main difference between recursive and explicit formulas in geometric sequences?

• Both formulas are identical in use

• Explicit formulas require the previous term, recursive formulas do not

• Recursive formulas are faster to compute

• Recursive formulas require the previous term, explicit formulas do not

Which formula directly calculates the nth term without needing previous terms?

• Explicit formula

• Recursive formula

• Quadratic formula

• Linear formula

What type of graph does a geometric sequence form when plotted?

• Logarithmic

• Exponential

• Linear

• Quadratic

If the 5th term of a geometric sequence is 80 and the 8th term is 5/4, what is the common ratio?

• 1/16

• 1/8

• 1/4

• 1/2

How do you solve for the first term when given two terms in a geometric sequence?

• By multiplying the two terms

• By using a system of equations

• By subtracting the two terms

• By adding the two terms

What is the 12th term of a geometric sequence if the first term is 20480 and the common ratio is 1/4?

• 10

• 5

• 20

• 40