What are the next two numbers in the pattern of numbers; 45, 15, 44, 17, 40, 20, 31, 25, …
Answers
The next two numbers are 15 and 32.
So the series is:
45, 15, 44, 17, 40, 20, 31, 25, 15,32
- In this case, two trends are being followed. Every alternate number follows a similar trend.
1. Considering the first set of numbers:
45, 44, 40,31,....
The difference between the consecutive numbers is : -1,-4,-9
As observed, this becomes a series of perfect squares.
1^2, 2^2, 3^2
Therefore, the next difference should be -16
So, the next number in the first series should be 15.
2. For the second alternate set:
15, 17, 20,25....
Here, the difference between the numbers are- 2, 3,5
Therefore, we observe that they are all prime numbers in increasing order. So, the next difference should be 7.
So, the next number in this series should be 32.
45, 15, 44, 17, 40, 20, 31, 25, 15, 32.....
Step-by-step explanation:
45, 15, 44, 17, 40, 20, 31, 25,.....
To interpret the series, we need to split the series into odd terms and even terms.
The even terms in the series follow a pattern while the odd terms in the series follow a different pattern.
Pattern for the odd terms of the series:
45, 44, 40, 31, ...
The pattern is that the next number is diminished by the square of numbers in sequence.
45 - 1² = 44
44 - 2² = 40
40 - 3² = 31
So the next term will be 31 - 4² = 31 - 16 = 15
Pattern for the odd terms of the series:
15, 17, 20, 25...
The pattern is that the next number is increased by the prime numbers in sequence.
15 + 2 = 17
17 + 3 = 20
20 + 5 = 25
So the next term will be 25 + 7 = 32
So the series will be 45, 15, 44, 17, 40, 20, 31, 25, 15, 32.....