Geometric Sequence and Series

Geometric Sequence and Series

By Nicole Stanziale

Multiple Choice

Which kind of sequence has a common ratio?

• Arithmetic
• Geometric

Multiple Choice

This image shows how a certain bacteria grows in a petri dish. What is the common ratio of this sequence?

• 4
• 3
• 2
• 6

Multiple Choice

The difference between two terms in an arithmetic sequence is called ___________________.

• Formula

• Common Ratio

• Common Difference

• Common Factor

Multiple Choice

What does r represent?

• Radical

• Common difference

• Common ratio

Multiple Choice

What does a₁ represent?

• Any term

• First term

• Last term

Multiple Choice

Daisy received $2 on her first birthday. Each year, the amount of money she received tripled. How much money will she receive on her 5^th birthday?

• $10

• $300

• $162

• $416

Multiple Choice

What is the nth term rule for the sequence:

11, 22, 44, 88...

• U_n = 2(11)^n-1

• U_n = 11x2

• U_n = 11(2)^n-1

Multiple Choice

Find the sum of the infinite geometric series, if it exists. $$\sum_{n=1}^{\infty}8\left(\frac{1}{5}\right)^{n-1}$$  

• 8

• 8/5

• 10

• Does not exist

Multiple Choice

Which of the series below is CONVERGENT?

• a₁=4, 1.5a_n-1, n≥2
• a_n=-n²- 8n +106
• a_n = 5/10ⁿ
• a_n = 5n + 6

Multiple Choice

Which of the following is DIVERGENT?

• 2+4+8+16+...

• 25+5+1+0.2+...

• 100+50+25+5+...

• 3(.25)ⁿ = A_n

Multiple Choice

$$\sum_{k=1}^{\infty}\left(\frac{4}{5}\right)^{k-1}$$  Find the sum of the series if it exists.

• 4/5

• 5

• 6.5

• Does not exist