Homework / 09/05

Question 9
What are the next two terms?
1, 1/2, 1/4, 1/8 ...

• 1/16, 1/32

• 1/10, 1/20

• 1/12, 1/24

• 1/15, 1/30

Answer explanation

The series given in the question follows a pattern where each term is half of the previous term. So, after 1, 1/2, 1/4, and 1/8, the next two terms would logically be 1/16 and 1/32. Hence, the correct answer is '1/16, 1/32'.

Question 7
What are the next two terms in the series?
1, 4, 9, 16, 25 ...

• 36, 49

• 30, 35

• 27, 36

• 35, 45

Answer explanation

The series in the question is a sequence of perfect squares. The pattern is as follows: 1 (1^2), 4 (2^2), 9 (3^2), 16 (4^2), 25 (5^2). Continuing this pattern, the next two terms are 36 (6^2) and 49 (7^2), which matches the correct answer.

Question 11
What are the next two terms in the series?
15, 12, 9, 6...

• 3, 0

• 4, 2

• 5, 3

• 3, 1

Answer explanation

The question is asking for the next two terms in the series of 15, 12, 9, 6. Observing the series, it decreases by 3 every time. Therefore, continuing this pattern, the next two terms would be 3 and 0, which matches the correct answer.

Question 15
What are the next two terms in the sequence?
Washington, Adams, Jefferson, ...

• Madison, Monroe

• Lincoln, Kennedy

• Roosevelt, Truman

• Bush, Obama

Answer explanation

The sequence given in the question follows the order of service of the Presidents of the United States. After Washington, Adams, and Jefferson, the next two presidents were Madison and Monroe. Hence, the correct answer is 'Madison, Monroe'.

Question 21
What would be the color of the fifteenth figure?

• Purple

• Teal

• Red

Question 27
Make a conjecture for the following scenario:
The sum of two odd numbers.

• The sum is always even

• The sum is always odd

• The sum is always prime

• The sum is always a multiple of 5

Answer explanation

The question asks for a conjecture about the sum of two odd numbers. The correct choice is that the sum is always even. This is because the sum of two odd numbers is always even. For example, 3+5=8, which is even. The other options are incorrect since the sum doesn't always result in an odd, prime or multiple of 5.

Question 29
Make a conjecture for the following scenario:
The product of two even numbers.

• Is always an even number

• Is always an odd number

• Can be either even or odd

• Is always a prime number

Answer explanation

The product of two even numbers is always an even number. This is because the multiplication of any two even numbers always results in another even number. Any other combinations can result in either even or odd numbers, but the product of two even numbers will always be even.

Question 39
Find the next two terms in the series: 1, 2, 5, 6, 9, ...

• 10, 13

• 11, 14

• 12, 15

• 10, 11

Answer explanation

The series in the question is increasing by 1, then by 3, then by 1, then by 3, and so on. This pattern is repeated throughout the series. After the last given term, 9, if we add 1, we get the next term, 10. And adding 3 to 10 gives us the next term, 13. So, the next two terms are 10 and 13.

Question 43
Find the next two terms for the following sequence:
0, 1/2, 3/4, 7/8, 15/16

• 31/32, 63/64

• 1/32, 1/64

• 16/17, 32/33

• 1, 2

Answer explanation

The given sequence is a series of fractions where the numerator is one less than the denominator, doubling with each step. Following this pattern, the next terms would be 31/32 and 63/64, where the numerator is 31 (one less than 32) and 63 (one less than 64) respectively.

Question 45
Predict the next term in the sequence:
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = ?

• 123454321

• 12345654321

• 123456321

• 123456789

Answer explanation

The given question is asking to predict the next term in a specific numeric sequence. As seen from the pattern, when we multiply 1, 11, 111 and 1111 by themselves, the results are palindromic numbers that ascend from one. Following this pattern, when we multiply 11111 by itself, the result is the palindromic number 12345654321.