Understanding Geometric Sequences

The video tutorial introduces geometric sequences, explaining how to identify them using the common ratio. It distinguishes between arithmetic and geometric sequences, demonstrates how to extend sequences, and graph them. The tutorial also covers formulating equations for geometric sequences and finding specific terms using these equations.

What is the main objective when learning about geometric sequences?

• To identify and extend arithmetic sequences

• To find the common difference in sequences

• To identify, extend, and graph geometric sequences

• To solve linear equations

How can you determine if a sequence is geometric?

• By adding the same number to each term

• By subtracting the first term from the last term

• By dividing any term by its previous term to find a common ratio

• By checking if the sequence is increasing

What is the common ratio of the sequence 8, 24, 72, 216?

• 2

• 3

• 4

• 5

If a sequence has a common ratio of 1/2, what type of sequence is it?

• Exponential

• Geometric

• Arithmetic

• Neither

What conclusion can be drawn if a sequence has neither a common ratio nor a common difference?

• It is an arithmetic sequence

• It is a geometric sequence

• It is neither arithmetic nor geometric

• It is both arithmetic and geometric

What is the next term in the geometric sequence 24, 48, 96?

• 72

• 192

• 144

• 120

When graphing a geometric sequence, what type of function does it form?

• Linear

• Quadratic

• Exponential

• Logarithmic

What is the formula for finding the nth term of a geometric sequence?

• First term / common ratio^(n-1)

• First term * common ratio^(n-1)

• First term + (n-1) * common ratio

• First term - (n-1) * common ratio

If the first term of a geometric sequence is 2 and the common ratio is 6, what is the 10th term?

• 20,155,392

• 15,000,000

• 10,077,696

• 12,345,678

What is the 7th term of a geometric sequence with a first term of 1 and a common ratio of -5?

• -31,250

• 31,250

• -15,625

• 15,625