Understanding Geometric Sequences

What is the first step in determining if a sequence is geometric?

• Subtract the first term from the second term

• Add the first two terms

• Multiply the first two terms

• Divide the second term by the first term

In a geometric sequence, what must be true about the common ratio?

• It must be different for each pair of terms

• It must be a fraction

• It must be the same for all pairs of consecutive terms

• It must be a negative number

How do you calculate the common ratio of a sequence?

• By adding the first term to the second term

• By multiplying the first term by the second term

• By subtracting the first term from the second term

• By dividing the second term by the first term

If the first term (a1) is 7 and the second term (a2) is 14, what is the common ratio?

• 4

• 3

• 2

• 1

Why is it unnecessary to divide every pair of terms to find the common ratio?

• Because the ratio is always 1

• Because the ratio changes with each pair

• Because it is too time-consuming

• Because the first two terms are enough to determine the ratio

What confirms that a sequence is geometric?

• The terms are all even numbers

• The sequence has more than five terms

• The common ratio is consistent across all terms

• The terms are all odd numbers

What is the common ratio of the geometric sequence?

-3, 12, -48, 192, -768, . . .

Mathematical Equivalence

ON

• -16
• -11
• -6
• -1
• 4
• -21
• -26
• -31
• 5