Select the number from among the given options that can replace the question mark (?) in the following series.
31, 35, 51, 87, 151, ?, 395
- A251
- B262
- C187
- D215
Solution & Step-by-step Explanation
Let's calculate the differences between consecutive terms in the series:
35−31=4
51−35=16
87−51=36
151−87=64
The differences are: 4,16,36,64.
Notice that these are squares of consecutive even numbers:
4=2
2
16=4
2
36=6
2
64=8
2
Following this logic, the next difference must be:
10
2
=100
So, the missing term is:
151+100=251
Let's verify with the next term:
251+12
2
=251+144=395
This matches the final term perfectly.
35−31=4
51−35=16
87−51=36
151−87=64
The differences are: 4,16,36,64.
Notice that these are squares of consecutive even numbers:
4=2
2
16=4
2
36=6
2
64=8
2
Following this logic, the next difference must be:
10
2
=100
So, the missing term is:
151+100=251
Let's verify with the next term:
251+12
2
=251+144=395
This matches the final term perfectly.