Quizizz worksheet featuring sequences and number patterns with multiple-choice questions.

Problem Analysis and Solution

The image contains a series of questions related to sequences and number patterns. Let's solve each question step by step.

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#### Question 1: How many houses will be in the 5th pattern?

Image Description:
- The sequence shows a pattern of houses:
- 1st pattern: 1 house
- 2nd pattern: 3 houses
- 3rd pattern: 6 houses

Pattern Analysis:
- The number of houses in each pattern appears to follow a triangular number sequence.
- Triangular numbers are given by the formula:
\[
T_n = \frac{n(n+1)}{2}
\]
where \( n \) is the position in the sequence.

Calculation for the 5th pattern:
\[
T_5 = \frac{5(5+1)}{2} = \frac{5 \times 6}{2} = 15
\]

However, the options provided are:
- A: 4
- B: 29
- C: 23
- D: 5

It seems there might be a misunderstanding in the pattern interpretation. Let's re-examine the visual pattern:
- 1st pattern: 1 house
- 2nd pattern: 3 houses
- 3rd pattern: 6 houses

The differences between consecutive terms are:
- \( 3 - 1 = 2 \)
- \( 6 - 3 = 3 \)

This suggests an increasing difference pattern. If we continue this:
- 4th pattern: \( 6 + 4 = 10 \)
- 5th pattern: \( 10 + 5 = 15 \)

Given the options, it seems there might be a misinterpretation. Let's assume the pattern is based on a different rule. If we consider the options, the closest logical fit (based on the increasing difference pattern) is:
\[
\boxed{C}
\]

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#### Question 2: What is the general term for this sequence?

Image Description:
- The sequence shows vertical lines:
- 1st term: 3 lines
- 2nd term: 5 lines
- 3rd term: 7 lines

Pattern Analysis:
- The number of lines increases by 2 for each subsequent term.
- This is an arithmetic sequence with the first term \( a = 3 \) and common difference \( d = 2 \).

General Term Formula for Arithmetic Sequence:
\[
T_n = a + (n-1)d
\]
Substitute \( a = 3 \) and \( d = 2 \):
\[
T_n = 3 + (n-1) \cdot 2 = 3 + 2n - 2 = 2n + 1
\]

Matching with Options:
- A: \( T_n = 2n \)
- B: \( T_n = 3 + 2n \)
- C: \( T_n = 2n + 1 \)
- D: \( T_n = 2n + 2 \)

The correct option is:
\[
\boxed{C}
\]

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#### Question 3: The terms in the number sequence 3, 6, 12, 24… are generated by:

Sequence Analysis:
- The sequence is: 3, 6, 12, 24, …
- Each term is obtained by multiplying the previous term by 2:
- \( 6 = 3 \times 2 \)
- \( 12 = 6 \times 2 \)
- \( 24 = 12 \times 2 \)

Matching with Options:
- A: adding 12
- B: multiplying by 2
- C: multiplying by 3
- D: adding 3

The correct option is:
\[
\boxed{B}
\]

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#### Question 4: The terms in the number sequence 128, 64, 32, 16, … are generated by:

Sequence Analysis:
- The sequence is: 128, 64, 32, 16, …
- Each term is obtained by multiplying the previous term by \( \frac{1}{2} \):
- \( 64 = 128 \times \frac{1}{2} \)
- \( 32 = 64 \times \frac{1}{2} \)
- \( 16 = 32 \times \frac{1}{2} \)

Matching with Options:
- A: multiplying by 2
- B: multiplying by \( \frac{1}{2} \)

The correct option is:
\[
\boxed{B}
\]

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Final Answers:

1. \(\boxed{C}\)
2. \(\boxed{C}\)
3. \(\boxed{B}\)
4. \(\boxed{B}\)