Identifying Geometric Sequences and Recursive Formulas

What defines a geometric sequence?

• A constant addition or subtraction between terms

• A pattern of alternating signs

• A constant ratio between consecutive terms

• Random differences between terms

Which sequence type involves multiplying by the same number each time?

• Arithmetic

• Linear

• Geometric

• Fibonacci

How do you find the common ratio in a geometric sequence?

• Multiply consecutive terms

• Divide a term by its preceding term

• Subtract consecutive terms

• Add consecutive terms

What is the common ratio if the sequence progresses from 2 to 6 to 18?

• 3

• 6

• 4

• 2

How can you verify the common ratio using a calculator?

• Subtraction of terms

• Addition of terms

• Division of consecutive terms

• Multiplication of the first term

What is the recursive formula for a geometric sequence?

• a(n) = a(1) + nr

• a(n) = a(n-1) * r

• a(n) = a(1) * r^n

• a(n) = a(n-1) + r

If a sequence starts at 7 and the next term is 21, what is the common ratio?

• 2

• 3

• 28

• 14

What is the common ratio if a sequence progresses from 40 to 20 to 10?

• 1.5

• 2

• 0.25

• 0.5

What does a negative common ratio indicate in a geometric sequence?

• The sequence will reset

• The sequence terms will alternate in sign

• The sequence will decrease

• The sequence will increase

In a geometric sequence, if the first term is 2 and the common ratio is -5, what is the third term?

• 10

• -10

• 50

• -50