Which number will replace the question mark (?) in the following series?
3, 8, 15, 25, 40, 62, 95, ?
- A141
- B114
- C144
- D111
Solution & Step-by-step Explanation
Let's find the difference between consecutive terms of the series:
8−3=5
15−8=7
25−15=10
40−25=15
62−40=22
95−62=33
Now, let's look at the differences: 5, 7, 10, 15, 22, 33.
Let's find the double difference (difference of differences):
7−5=2
10−7=3
15−10=5
22−15=7
33−22=11
The double differences are 2, 3, 5, 7, 11, which are consecutive prime numbers!
The next prime number after 11 is 13.
Therefore, the next difference will be:
33+13=46
The next term in the series will be:
95+46=141
8−3=5
15−8=7
25−15=10
40−25=15
62−40=22
95−62=33
Now, let's look at the differences: 5, 7, 10, 15, 22, 33.
Let's find the double difference (difference of differences):
7−5=2
10−7=3
15−10=5
22−15=7
33−22=11
The double differences are 2, 3, 5, 7, 11, which are consecutive prime numbers!
The next prime number after 11 is 13.
Therefore, the next difference will be:
33+13=46
The next term in the series will be:
95+46=141