Question

Use inductive reasoning to predict the next number in each list.
1. 4,8,12,16,20,24,?

2. 5,11,17,23,29,35,?

3. 3,5,9,15,23,33,?

4. 1,8,27,64,125,?

5. 1,4,9,16,25,36,49,?

Answer 1

Answer:

1. 28

2. 41

3. 45

4. ??

5. 64

Answer 2

Given:

A series of numbers,

1. 4, 8,12,16, 20, 24

2. 5,11,17, 23, 29, 35  

3. 3, 5, 9,15,23,33  

4. 1, 8, 27, 64,125  

5. 1, 4, 9,16, 25, 36, 49  

To Find:

The next number of every sequence.

Solution:

The given question can be solved by developing a common logic between every term of the series.

1. 4, 8,12,16, 20, 24

• The second term is equal to the first term + 4,

• The third term is equal to the second term + 4,

• The fourth term is equal to the third term + 4,

• The fifth term is equal to the fourth term + 4,

• The sixth term is equal to the fifth term + 4,

• Hence, the seventh term is equal to the value of sixth term +4,

= > Next number of the sequence = 24+4,

= > Next number = 28.

2. 5,11,17, 23, 29, 35

• The second term is equal to the first term + 6,

• The third term is equal to the second term + 6,

• The fourth term is equal to the third term + 6,

• The fifth term is equal to the fourth term + 6,

• The sixth term is equal to the fifth term + 6,

• Hence, the seventh term is equal to the value of sixth term +6,

= > Next number of the sequence = 35+6,

= > Next number = 41.

3. 3, 5, 9,15,23,33

• The second term is equal to the first term + 2,

• The third term is equal to the second term + 4,

• The fourth term is equal to the third term + 6,

• The fifth term is equal to the fourth term + 8,

• The sixth term is equal to the fifth term + 10,

• Hence, the seventh term is equal to the value of sixth term +12,

= > Next number of the sequence = 33+12,

= > Next number = 45.

 

4. 1, 8, 27, 64,125  

• The first term of the sequence is also written as 1 ^3.

• The second term of the sequence is also written as 2 ^3.  

• The third term of the sequence is also written as 3 ^3.

• The fourth term of the sequence is also written as 4 ^3.

• The fifth term of the sequence is also written as 5 ^3.

• Hence, the sixth term of the sequence is written as,

= > Next term of the sequence = 6 ^ 3,

= > Next term of the sequence = 216.

5. 1, 4, 9,16, 25, 36, 49

• The first term of the sequence is also written as 1 ^2.

• The second term of the sequence is also written as 2 ^2.  

• The third term of the sequence is also written as 3 ^2.

• The fourth term of the sequence is also written as 4 ^2.

• The fifth term of the sequence is also written as 5 ^2.

• The sixth term of the sequence is also written as 6 ^2.

• The seventh term of the sequence is also written as 7 ^2.

• Hence, the sixth term of the sequence is written as,

= > Next term of the sequence = 8 ^ 2,

= > Next term of the sequence = 64.