Geometric Sequences

What does r represent?

• Radical

• Common difference

• Common ratio

Find the common ratio for the geometric sequence.

• 10
• 1/2
• 2
• 4

Answer explanation

DIVIDE any term by the term BEFORE

Find the common ratio for the geometric sequence.

• 1
• -1
• 7
• -7

Answer explanation

DIVIDE any term by the term BEFORE

Find the common ratio for the geometric sequence.

• -4
• 4
• 1/4
• -1/4

Answer explanation

DIVIDE any term by the term BEFORE

What does a₁ represent?

• Any term

• First term

• Last term

Write the explicit formula for the geometric sequence.

• a_n = 4(3)^n-1
• a_n = 3(4)^n-1
• a_n = -4(3)^n-1
• a_n = 3(-4)^n-1

Answer explanation

Find r: DIVIDE any term by the term BEFORE

a_n=a₁(r)^n-1

a₁=3 and r=-4

a_n=3(-4)^n-1

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

• 20, 100, 500, 2500
• 5, 20, 80, 320
• 4, 20, 100, 500
• 4, 9, 14, 19

Answer explanation

a₁=4(5)^1-1=4

a₂=4(5)^2-1=20

a₃=4(5)^3-1=100

a₄=4(5)^4-1=500

What is the 14th term of the geometric sequence?

• 14,348,907
• 4,782,969
• 1,594,323
• 45

Answer explanation

Find r: DIVIDE any term by the term BEFORE

a₁=3 and r=3

Write the equation: a_n=a₁(r)^n-1

a_n=3(3)^n-1

Evaluate for n=14

a₁₄=3(3)^14-1

Given the sequence:

125, 25, 5, ....

Write the rule a_n using the geometric sequence formula:

• a_n = (125)(1/5)^(n-1)

• a_n = 625(1/5)^(n-1)

• a_n = 625(5)^(n-1)

• a_n = 125 + 5n

Answer explanation

Find r: DIVIDE any term by the term BEFORE

Write the equation: a_n=a₁(r)^n-1

a₁=125 and r=1/5

a_n=125(1/5)^n-1

Find a₁₂ in the sequence -1, -3, -9, -27, ...

• -177,147
• -19,683
• -59,049
• 118,098

Answer explanation

Find r: DIVIDE any term by the term BEFORE

Write the equation: a_n=a₁(r)_n-1

a₁=-1 and r=3

a_n=-1(3)^n-1

a₁₂=-1(3)^12-1