Math 10 EVM Week 4 Quiz
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Questions and Answers

What is the temperature of the hot tub after the first hour if it increases by 10%?

  • 90.75ºF
  • 75ºF
  • 82.5ºF (correct)
  • 84ºF

What is the common ratio for the geometric sequence starting with 125 and ending with 64?

  • 0.75
  • 0.9
  • 0.5
  • 0.8 (correct)

If the temperature of the hot tub is 75ºF initially, what is the formula to find the temperature after 'n' hours?

  • $a_n = 75(1.1)^{n-1}$ (correct)
  • $a_n = 75(0.1)^n$
  • $a_n = 75 + 10n$
  • $a_n = 75(1.1)^n$

How many bacteria will there be after 12 hours if a culture of bacteria doubles every 2 hours starting from 500?

<p>32000 (A)</p> Signup and view all the answers

What will be the temperature of the hot tub after 2 hours?

<p>90.75ºF (C)</p> Signup and view all the answers

What is the increase in temperature after the third hour?

<p>9.075ºF (D)</p> Signup and view all the answers

If the hot tub temperature increases by 10% each hour starting at 75ºF, what will the temperature be after 3 hours?

<p>83.25ºF (C)</p> Signup and view all the answers

What is the 4th term in the geometric sequence defined by $a_n = a_1 r^{n-1}$ with $a_1 = 1$ and $r = 2$?

<p>8 (C)</p> Signup and view all the answers

How is the growth factor represented in terms of the percentage increase?

<p>1.1 (B)</p> Signup and view all the answers

Calculate the temperature of the hot tub after three hours, starting at 75ºF.

<p>99.825ºF (A)</p> Signup and view all the answers

Which of the following sequences represents a geometric sequence?

<p>2, 4, 8, 16 (B)</p> Signup and view all the answers

What is the rate of increase for a geometric sequence if the first term is 100 and the second term is 80?

<p>0.8 (C)</p> Signup and view all the answers

What represents the first term in this geometric sequence starting from 75ºF?

<p>75ºF (D)</p> Signup and view all the answers

In a geometric sequence, what does 'r' denote if the temperature increases by 10% each hour?

<p>1.1 (D)</p> Signup and view all the answers

In a geometric sequence, if the first term is 1 and the common ratio is -2, what is the 5th term?

<p>-32 (A)</p> Signup and view all the answers

Which of the following pairs of numbers between 125 and 64 can form a geometric sequence with a common ratio?

<p>100 and 80 (A)</p> Signup and view all the answers

What is the common ratio of the geometric sequence given the 2nd term is 20 and the 6th term is 320?

<p>4 (B)</p> Signup and view all the answers

What is the 1st term of the geometric sequence if the 2nd term is 20 and the common ratio is 4?

<p>10 (A)</p> Signup and view all the answers

If the 1st term of a geometric sequence is 5 and the common ratio is 4, what is the 6th term?

<p>2560 (D)</p> Signup and view all the answers

What is the general formula for the nth term of a geometric sequence?

<p>$a_n = a_1 r^{n-1}$ (D)</p> Signup and view all the answers

If a geometric sequence has its 2nd term as 20, what is the relationship between the 1st and 3rd terms?

<p>The 3rd term is the 1st term multiplied by the square of the common ratio (D)</p> Signup and view all the answers

Which of the following statements about geometric means in a sequence is correct?

<p>Geometric means can be negative if the ratio is negative. (A)</p> Signup and view all the answers

If a geometric sequence starts with an initial term of 3 and ends with 75, what could be a possible common ratio?

<p>5 (A)</p> Signup and view all the answers

How many terms can exist between the first and last term of a geometric sequence if the initial term is 3 and the last term is 75 with a common ratio of 5?

<p>4 (C)</p> Signup and view all the answers

What is the common ratio of the geometric sequence 3, 6, 12, 24?

<p>2 (C)</p> Signup and view all the answers

How many bacteria will there be after 12 hours if a culture doubles every 2 hours, starting with 500 bacteria?

<p>32000 (D)</p> Signup and view all the answers

Which of the following sequences is NOT a geometric sequence?

<p>1, 3, 6, 10 (A)</p> Signup and view all the answers

What is the nth term of the geometric sequence if a1 = 10 and r = 0.5?

<p>10 * (1/2)^{(n-1)} (D)</p> Signup and view all the answers

Which of the following best describes a geometric progression?

<p>A sequence where terms multiply a constant number (C)</p> Signup and view all the answers

If a geometric sequence has a common ratio of -2, what is the 3rd term if the first term is 4?

<p>-16 (D)</p> Signup and view all the answers

In a geometric sequence, what does the term 'geometric mean' refer to?

<p>The product of two numbers when taken under the square root (A)</p> Signup and view all the answers

What is the formula for the nth term of a geometric sequence?

<p>$a_n = a_1 r^{n-1}$ (D)</p> Signup and view all the answers

If the first term of a geometric sequence is 5 and the common ratio is 3, what is the 3rd term?

<p>45 (C)</p> Signup and view all the answers

What is the common ratio (r) if the 2nd term of a geometric sequence is 12 and the 6th term is 192?

<p>4 (C)</p> Signup and view all the answers

What would be the value of the 6th term if the first term is -3 and the common ratio is -2?

<p>-96 (D)</p> Signup and view all the answers

What is the 7th term of the sequence 2, 6, 18, 54, 162?

<p>1458 (D)</p> Signup and view all the answers

If the 1st term is 8 and the common ratio is 0.5, what is the 5th term of this geometric sequence?

<p>1 (D)</p> Signup and view all the answers

In a geometric sequence, if the 3rd term is 16, 2nd term is 8, and 1st term is x, what is the value of x?

<p>4 (D)</p> Signup and view all the answers

Flashcards

Geometric Sequence

A sequence where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Common Ratio (r)

The constant number by which each term in a geometric sequence is multiplied to get the next term.

nth term of a geometric sequence

A formula to find any term in a geometric sequence using the first term and the common ratio. For example: a(n) = a(1) â‹… r^(n-1)

Geometric Sequence Example

A sequence such as 2, 6, 18, 54, ... where each term is 3 times the previous term.

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Arithmetic Sequence vs Geometric Sequence

Arithmetic sequences add a constant to get the next term, while geometric sequences multiply by a constant.

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Identifying a Geometric Sequence

Check if the ratio between consecutive terms is constant. If it is, it's a geometric sequence.

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Geometric Mean

A geometric mean is a number between two given numbers such that the numbers form a geometric sequence.

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Solving Geometric Sequence Problems

Use the formula for the nth term (a(n) = a(1) â‹… r^(n-1)) and the concept of common ratio to find missing terms, total terms etc.

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Geometric Sequence Formula

The nth term of a geometric sequence is determined by the formula an = a1 * r^(n-1), where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.

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nth Term (an)

The term in a sequence that is at position n.

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First Term (a1)

The first number in a geometric sequence.

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Finding the 6th term

Solving for a specific term in a sequence by applying the formula for the nth term in a geometric sequence.

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Find a(n)

Using the formula an = a1 * r^(n-1) to get the nth term; to find a term in a geometric sequence.

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Finding first term (a1)

Solving for the first term in a geometric sequence given two terms and their positions in the sequence.

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Geometric Sequence 1st term

The first number in a geometric sequence. It's multiplied by the common ratio (r) to get each subsequent term.

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Geometric Sequence 2nd term

The second number in the geometric sequence. Calculated by multiplying the 1st term by the common ratio once.

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Geometric Sequence Common Ratio

The value that is multiplied repeatedly to get the next terms in a geometric sequence.

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Geometric Sequence nth term

The general formula for any term (n) in the sequence. an = a1 * r^(n-1)

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Find a missing geometric term

Given two terms in a geometric sequence, find the intervening terms (geometric means) and the first term.

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Identify common ratio

Identify the value (r) that, when multiplied by each term of a sequence, results in the subsequent term.

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What's the common ratio?

The constant factor used to multiply each term in a geometric sequence to get the next term.

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Bacteria Growth

An example of a real-world situation where a geometric sequence is used to model the doubling of bacteria every fixed time interval.

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Hot Tub Temperature Increase

A practical example where a geometric sequence is used to model a percentage increase in temperature over time.

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Geometric Sequence: Number of Terms?

To find the number of terms in a geometric sequence, you can use the formula: a(n) = a(1) â‹… r^(n-1). You know a(n) (the last term), a(1) (the first term), and r (the common ratio), so you can solve for n.

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Finding Missing Terms

Using the geometric sequence formula, you can find any missing term in a sequence by knowing the first term, the common ratio, and the term number of the missing term.

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Geometric Sequence vs. Arithmetic Sequence

A geometric sequence is characterized by a constant ratio between consecutive terms, while an arithmetic sequence is characterized by a constant difference between consecutive terms.

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Temperature After 3 Hours

The temperature of the hot tub after 3 hours, given an initial temperature and a percentage increase each hour - this can be calculated using the nth term formula in a geometric sequence.

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Finding the Temperature After a Specific Time

Using the nth term formula of a geometric sequence to calculate the temperature of the hot tub after a specific time, given the initial temperature and the percentage increase per hour.

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Real-World Examples of Geometric Sequences

Geometric sequences can be found in many real-world scenarios, such as the growth of bacteria, compound interest calculations, and radioactive decay.

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Study Notes

Math 10 EVM Information

  • Course: Math 10 EVM
  • Instructor: Ma'am Hanie Banzuelo
  • Quarter: 2
  • Week: 4
  • Meeting: 2nd

Weekly Instructional Schedule for Week 4

  • Week 4
  • Topics:
    • Discussion of Chapter & Unit Test Test 2.1: Arithmetic Sequences, Series & Means
    • T2.4. Geometric Sequence and Means
    • T2.5. Geometric Series
    • Bridge Day NMP Remediation - Translation and Writing Equations

Learning Competencies for the Day

  • C.1.4. Illustrates a geometric sequence.
  • C.1.5 Differentiates a geometric sequence from an arithmetic sequence.
  • C.1.6. Determines geometric means, nth term of a geometric sequence.
  • C.1.7. Solves problems involving sequences.

Bacteria Culture Problem

  • Background: A culture of bacteria doubles every 2 hours
  • Initial Bacteria: 500
  • Question: How many bacteria will there be in 12 hours?
  • Answer: 32,000 bacteria

Geometric Sequence Formula

  • Formula: an = a1rn-1
  • Explanation: an represents the nth term, a1 represents the first term, r represents the common ratio, and n represents the number of terms.

Examples of Geometric Sequences

  • 1, 2, 4, 8, 16
  • 80, -40, 20, -10, 5
  • 2, 6, -18, -54, 162
  • (x+y), (x+y)², (x+y)³, (x+y)4, (x+y)5

Determining Geometric Sequences

  • Method: Check if the ratio between consecutive terms is constant.

Geometric Means

  • Definition: The terms between any two terms of a geometric sequence.
  • Formula: m = √(a1an) where m is the geometric mean, a1 is the first term and an is the nth term.

Additional Exercises

  • Various problems involving finding the nth term, common ratio, and first term of geometric sequences.

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Related Documents

Math 10 Geometric Sequences and Means PDF

Description

Test your knowledge on arithmetic and geometric sequences in Math 10 EVM for Week 4. This quiz covers concepts such as identifying sequences, solving related problems, and understanding means. Challenge yourself with practical applications of these mathematical principles.

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