﻿ Number Pattern Worksheets | Problems & Solutions

# Number Pattern Worksheets

Number Pattern Worksheets
• Page 1
1.
Which set of ordered pairs satisfies the rule "the first number is two less than thrice the second number"?
 a. {(12, 6), (15, 7), (18, 8)} b. {(20, 6), (23, 7), (26, 8)} c. {(9, 6), (11, 7), (13, 8)} d. {(16, 6), (19, 7), (22, 8)}

#### Solution:

First number = (3 times the second number) minus 2 = (3 × second number) - 2
[The first number is two less than thrice the second number.]

It is enough to check only one ordered pair from each choice to check if it satisfies the given rule. If one of them satisfies the rule, then check the other two pairs in the respective set.

15 ≠ (3 × 7) - 2 (= 19)
[Consider the ordered pair (15, 7) in choice A and use the rule.]

26 ≠ (3 × 8) - 2 (= 22)
[Consider the ordered pair (26, 8) in choice B and use the rule.]

9 ≠ (3 × 6) - 2 (= 16)
[Consider the ordered pair (9, 6) in choice C and use the rule.]

22 = (3 × 8) - 2 = 22
[Consider the ordered pair (22, 8) in choice D and use the rule.]

19 = (3 × 7) - 2 = 19 and 16 = (3 × 6) - 2 = 16
[Check the other two ordered pairs as well.]

So choice D satisfies the given rule.

2.
Sheena is making a design in the form of a rectangle, with small red and green cubes. The design is 9 cubes wide. She arranges 3 rows of green cubes, 2 rows of red cubes, 3 rows of green cubes and so on. If she wants to make 100 rows of cubes in all, how many red cubes will she need?
 a. 360 b. 540 c. 600 d. 500

#### Solution:

The rectangular design is 100 cubes long and 9 cubes wide.
[Length of the rectangle = total number of rows.]

The arrangement of cubes along the 100 rows is: 3G2R3G2R. . . or the pattern is 3, 2, 3, 2, . . .
[There are 3 rows of green cubes, 2 rows of red cubes, 3 rows of green cubes and so on.]

There are 3 × 20 = 60 rows of green cubes and 2 × 20 = 40 rows of red cubes.
[Group the 3 rows of green cubes and 2 rows of red cubes. You get 100 / (3+2)= 20 such groups.]

So, number of red cubes required = 40 × 9 = 360.
[Each row is 9 cubes wide. So, 40 rows of red cubes will have (40 Ãƒâ€” 12) cubes in it.]

3.
Which rule could be used to generate the ordered pairs in the table?
 $x$ $y$ 2 4 4 5 6 6 8 7
 a. $x$ = $y$ - 2 b. $y$ = 2$x$ c. $x$ = $\frac{y}{2}$ d. $y$ = $\frac{x}{2}$+ 3

#### Solution:

Substitute any one of the ordered pairs in the table into each rule.

If the selected ordered pair satisfies any of the rules, then check if the rest of the ordered pairs satisfy the same rule. The rule that is satisfied by all four ordered pairs would be the answer.

Consider the ordered pair (6, 6).

6 ≠ 6 - 2 (= 4)
[Consider choice A = x = y - 2.]

6 ≠ 2 × 6 (= 12)
[Consider choice B = y = 2x.]

6 ≠ 6 / 2(= 3)
[Consider choice C = x = y / 2. ]

6 = 6 / 2+ 3 = 3 + 3 = 6
[Consider choice D = y = x / 2+ 3.]

So, the rule y = x / 2+ 3 works fine with the ordered pairs in the table.

4.
Sarah opened her math textbook. The product of the page numbers she saw was 210. What were the page numbers?
 a. 5, 42 b. 14, 15 c. 10, 21 d. 7, 30

#### Solution:

If n is one number then the other is either (n + 1) or (n - 1).
[When someone opens a book, they see two consecutive numbers as page numbers..]

n(n + 1) = 210 or (n - 1)n = 210
[The product of the page numbers Sarah saw was 210.]

Factors of 210 are: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, . . and a few more.
[Listing the factors would help identify the two consecutive numbers.]

14 and 15 are the two consecutive numbers that multiply to give 210.

So, the page numbers that Sarah saw were 14 and 15.

5.
Write a rule to describe the sequence. 8, 11, 14, . . .

#### Solution:

The first term of the number pattern is 8.

In the number pattern, 3 is Added to the preceding term to obtain the next term.

6.
Which of the following numbers complete the pattern?
14, 19, 24, ___, 34, 39...
 a. 25 b. 27 c. 29 d. 26

#### Solution:

14, 19, 24, ___, 34, 39...
[Given pattern.]

Using the number chart, start coloring from the first number that is 14 and then color 19, 24, 34, and 39.

This tells that the pattern is to skip count by 5's.

So, the missing number is found by adding 5 to 24.

Hence, we get 29.

7.
Complete the pattern.
6,000, 600, 60, 6, 0.6, ____
 a. 0.6 b. 0.606 c. 0.06 d. 0.006

#### Solution:

Each number in the sequence is divided by 10 to get the next number.

Therefore, to get the next number divide 0.6 by 10.

0.6 / 10 = 0.06

Therefore, 0.06 is the next number in the given pattern.

8.
Which of the expressions will help you to find the $n$th term in the sequence?
3, 9, 27, 81, . . .
 a. $n$2 b. 3$n$ c. $n$ + 3 d. 2$n$ + 1

#### Solution:

Each term in the given sequence is multiplied by 3, so, the nth term is 3n.

9.
Identify the missing term in the pattern.
1, 2, 4, 8, ____, 32, . . .
 a. 16 b. 22 c. 12 d. 10

#### Solution:

The rule for the pattern is to multiply by 2 for each succeeding term.

So, the missing term in the pattern is 16.

10.
Which of the following statements best suits for the table?
 Number of hours 1 2 3 4 Parking rates $2.00$2.75 $3.50$4.25
 a. Parking rate for every additional hour decreases by $2. b. Parking rate for every additional hour increases by$2. c. Parking rate for every vehicle increases by $0.75. d. Parking rate for every additional hour increases by$0.75.

#### Solution:

The table indicates an amount of $0.75 increases for every additional hour. So, the table best suits the statement 'Parking rate for every additional hour increases by$0.75'.