Geometric Series

Geometric Sequence

by Ma'am Julie Lacay

​Geometric Sequence

​It is a sequence whose next term is obtained by multiplying a constant number called the common ratio.

​​ Example:

​ 3, 6, 12, 24, ...

​ -1000, 500, -250, 125, ..

​Finding the NTH Term of Geometric Sequence

​ Use this formula:

​ a_n = a₁ r^n-1 where a_n = last term

​ a₁ = first term

​ r = common ratio

​ n = no. of terms

Multiple Choice

What does r represent in the geometric sequence formula?

• Radical

• Common difference

• Common ratio

Multiple Choice

What does a₁ represent?

• Any term

• First term

• Last term

Multiple Choice

What are the next 3 terms in the following geometric sequence:

5, -10, 20, ___, ___, ___, ...

• 30, -40, 50

• -40, 80, -160

• 40, -80, 160

• -40, 60, -80

Multiple Choice

Find the 10th term of the geometric sequence 2, -6, 18, ..., which of the following solutions below will arrive to the correct answer?

• a₁₀ = 2 ( 3)¹⁰

• a₁₀ = 2 ( -3)¹⁰

• a₁₀ = 2 ( 3)⁹

• a₁₀ = 2 ( -3)⁹

Multiple Select

Given a geometric sequence of 3/4, 3, 12, ... What are the values of a₁ and r ?

• a₁ = 3/4, r = 1/4

• a₁ = 3/4, r = 4

• a₁ = 3, r = 1/4

• a₁ = 3, r = 4

Multiple Choice

What is the 8th term of the geometric sequence 3, -6, 12, ...?

• 765

• 384

• - 384

• - 765

Multiple Choice

Find the 6th term of the sequence  3, -6, 12, ...?

• -192

• 48

• -96

• 96

Multiple Choice

Which of the following is a geometric sequence whose first term is 5 and whose common ratio is 2

• 5, 7, 9, 11, ...

• 5, 10, 15, 20, ...

• 5, 10, 20, 40, ...

• 2, 10, 50, 250,.