All the solutions provided in **McGraw Hill Math Grade 4 Answer Key PDF Chapter 7 Lesson 3 Sequences** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 4 Answer Key Chapter 7 Lesson 3 Sequences

**Math in My World
**Example 1

Crystal starts reading her book on Monday. She reads 25 pages on the first day. Each day, she reads 25 pages. How many total pages will she have read by Tuesday, Wednesday, Thursday, and Friday?

The first term of the sequence is 25.

The rule is add 25.

Extend the pattern.

So, Crystal will have read ____ pages by Tuesday, ___ pages by Wednesday, ___ pages by Thursday, and ___ pages by Friday.

Answer:

So, Crystal will have read 50 pages by Tuesday, 75 pages by Wednesday, 100 pages by Thursday, and 125 pages by Friday.

Explanation:

Number of pages on the first day she reads = 25.

Number of pages each day she reads = 25.

Number of pages each day she reads on Monday = Number of pages on the first day she reads = 25.

Number of pages each day she reads on Tuesday = Number of pages each day she reads on Monday + Number of pages each day she reads

= 25 + 25

= 50.

Number of pages each day she reads on Wednesday = Number of pages each day she reads on Tuesday + Number of pages each day she reads

= 50 + 25

= 75.

Number of pages each day she reads on Thursday = Number of pages each day she reads on Wednesday + Number of pages each day she reads

= 75 + 25

= 100.

Number of pages each day she reads on Friday = Number of pages each day she reads on Thursday + Number of pages each day she reads

= 100 + 25

= 125.

Example 2

The first term of a sequence is 65. The rule of the sequence is subtract 4. Find the next four terms in the sequence. Then make observations about the pattern.

1. Find the next four terms.

The next four terms in the sequence are ___, ____, ___, and ____

2. Make observations about the pattern.

Circle whether the terms are all odd or even. odd even

Circle whether the terms increase or decrease. increase decrease

Extend the pattern to a total of 10 terms.

65, ____, ___, ___, ___, ___, ___, ___, ___, ___

Make another observation about the pattern.

The ones digits repeat the pattern 5, 1, ___, ____, and ____

Answer:

Observations about the pattern:

Explanation:

The first term of a sequence is 65.

The rule of the sequence is subtract 4.

Next four terms in the sequence:

61 – 4 = 57.

57 – 4 = 53.

53 – 4 = 49.

49 – 4 = 45.

Next Six terms in the sequence:

45 – 4 = 41.

41 – 4 = 37.

37 – 4 = 33.

33 – 4 = 29.

29 – 4 = 25.

25 – 4 = 21.

The pattern to a total of 10 terms: 65, 57, 53, 49, 45, 41, 37, 33, 29, 25, 21.

Another observation about the pattern:

The ones digits repeat the pattern 5, 1, 7, 3, and 9.

**Talk Math**

How does the operation of a rule affect the terms of a sequence?

Answer:

The operation of a rule affect the terms of a sequence as it helps to find any term in the problem.

Explanation:

An operation is a mathematical action. Addition, subtraction, multiplication, division, and calculating the root are all examples of a mathematical operation

**Guided Practice
**

**Extend each pattern by four terms. Write an observation about the pattern.**

Question 1.

Rule: add 7

Pattern: 8, ___, ___, ___, ___

Observation: ________

Answer:

Pattern: 8, 15, 22, 29, 36.

Observation: It is observed that four numbers are prime and 1 is composite number.

Explanation:

Rule: add 7

8 + 7 = 15.

15 + 7 = 22.

22 + 7 = 29.

29 + 7 = 36.

Pattern: 8, 15, 22, 29, 36.

Question 2.

Rule: subtract 10

Pattern: 90, ___, ___, ___, ____

Observation: __________

Answer:

Pattern: 90, 80, 70, 60, 50.

Observation: It is observed the numbers are Multiplies of 10.

Explanation:

Rule: subtract 10

90 – 10 = 80.

80 – 10 = 70.

70 – 10 = 60.

60 – 10 = 50.

Pattern: 90, 80, 70, 60, 50.

### McGraw Hill My Math Grade 4 Chapter 7 Lesson 3 My Homework Answer Key

**Practice**

**Extend each pattern by four terms. Write an observation about the pattern.
**Question 1.

Rule: add 8

Pattern: 5, ___, ___, ___, ____

Observation: ________

Answer:

Pattern: 5, 13, 21, 29, 37.

Observation: It is observed all numbers are prime numbers.

Explanation:

Rule: add 8

5 + 8 = 13.

13 + 8 = 21.

21 + 8 = 29.

29 + 8 = 37.

Pattern: 5, 13, 21, 29, 37.

Question 2.

Rule: multiply by 2

Pattern: 3, ___, ___, ___, ____

Observation: __________

Answer:

Pattern: 3, 6, 12, 24, 48.

Observation: It is observed all numbers are even numbers.

Explanation:

Rule: multiply by 2

3 × 2 = 6.

6 × 2 = 12.

12 × 2 = 24.

24 × 2 = 48.

Question 3.

Rule: subtract 20

Pattern: 175, ___, ___, ____

Observation: ________

Answer:

Pattern: 175, 155, 135, 115, 95.

Observation: It is observed all numbers are multiplies of 5.

Explanation:

Rule: subtract 20

175 – 20 = 155.

155 – 20 = 135.

135 – 20 = 115.

115 – 20 = 95.

Question 4.

Extend the pattern below by four terms. Write an observation about the pattern.

Rule: multiply by 10

Pattern: 26, ___, ___, ____, ____

Observation: ___________

Answer:

Pattern: 26, 260, 2600, 26000, 260000.

Observation: It is observed all numbers are even and are increasing.

Explanation:

Rule: multiply by 10

26 × 10 = 260.

260 × 10 = 2,600.

2,600 × 10 = 26,000.

26,000 × 10 = 2,60,000.

**Problem Solving
**Question 5.

**Mathematical PRACTICE 8 Look for a Pattern**Brad puts an equal amount of money in his savings account once a month. He started with $25. The next month, he had $35 in his account. Two months after that, he had $55 in his account. How much money will Brad have in his account after 6 months? Describe a rule. Then solve.

Answer:

Amount of savings the next six months he had in his account = $175.

Explanation:

Amount of savings he started = $25.

Amount of savings the next month he had in his account = $35 .

Amount of savings on three months he had in his account = $55.

Amount of savings in a month he did = Amount of savings the next month he had in his account – Amount of savings he started

= $35 – $25

= $10.

Amount of savings the next three months he had in his account = Amount of savings in two month he did + (Number of months + Number of months)

= $35 + (2 × Amount of savings in a month he did)

= $35 + (2 × $10)

= $35 + $20

= $55.

Amount of savings the next four months he had in his account = Amount of savings in three months he did + (Number of months + Amount of savings in a month he did)

= $55 + (3 × $10)

= $55 + $30

= $85.

Amount of savings the next five months he had in his account = Amount of savings in four months he did + (Number of months + Amount of savings in a month he did)

= $85 + (4 × $10)

= $85 + $40

= $125.

Amount of savings the next six months he had in his account = Amount of savings in five months he did + (Number of months + Amount of savings in a month he did)

= $125 + (5 × $10)

= $125 + $50

= $175.

Question 6.

On Monday, a toy store sold 4 race cars. On Tuesday, it sold 8 race cars. On Wednesday, it sold 16 race cars. . Suppose this pattern continues. How many race cars will be sold on Friday? Describe a rule. Then solve.

Answer:

Number of race cars a toy store sold on Friday = 64.

Explanation:

Number of race cars a toy store sold on Monday = 4.

Number of race cars a toy store sold on Tuesday = 8.

Number of race cars a toy store sold on Wednesday = 16

Number of race cars a toy store sold on Thursday = Number of race cars a toy store sold on Wednesday × 2

= 16 × 2

= 32.

Number of race cars a toy store sold on Friday = Number of race cars a toy store sold on Thursday × 2

= 32 × 2

= 64.

**Vocabulary Check
**

**Write a vocabulary word to complete each sentence.**

sequence term

Question 7.

Each number in a numeric pattern is a ____

Answer:

Each number in a numeric pattern is a term.

Explanation:

A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted. Some terms contain variables with a number in front of them.

Question 8.

A ____ is the ordered arrangement of terms that make up a pattern.

Answer:

A sequence is the ordered arrangement of terms that make up a pattern.

Explanation:

A Sequence is a list of things (usually numbers) that are in order.

**Test Practice
**Question 9.

Identify the next term in the sequence. 171, 141, 111, 81, ____

A. 61

B. 51

C. 41

D. 31

Answer:

51 is the next term in the sequence.

B. 51.

Explanation:

Sequence: 171, 141, 111, 81, ??

171 – 141 = 30.

141 – 111 = 30.

111 – 81 = 30.

81 – 30 = 51.