Select the number from among the given options that can replace the question mark (?) in the following series.
1, 5, 10, 23, 63, 167, ?
- A396
- B369
- C862
- D826
Solution & Step-by-step Explanation
Let's find the step differences between the terms:
5−1=4
10−5=5
23−10=13
63−23=40
167−63=104
Now let's examine the sequence of differences: 4,5,13,40,104
Let's find the second-level differences:
5−4=1=1
3
13−5=8=2
3
40−13=27=3
3
104−40=64=4
3
Following this logic, the next second-level difference must be 5
3
=125.
The next first-level difference will be 104+125=229.
Therefore, the missing number is 167+229=396.
5−1=4
10−5=5
23−10=13
63−23=40
167−63=104
Now let's examine the sequence of differences: 4,5,13,40,104
Let's find the second-level differences:
5−4=1=1
3
13−5=8=2
3
40−13=27=3
3
104−40=64=4
3
Following this logic, the next second-level difference must be 5
3
=125.
The next first-level difference will be 104+125=229.
Therefore, the missing number is 167+229=396.