In the following question, select the missing number from the given series.
5, 29, 73, 141, 237, 365, ?
- A529
- B422
- C500
- D525
Solution & Step-by-step Explanation
Let's find the differences between adjacent terms in the series:
29−5=24
73−29=44
141−73=68
237−141=96
365−237=128
Now let's examine the differences of these differences (second layer of difference):
44−24=20
68−44=24
96−68=28
128−96=32
The second-layer differences increase by +4 each time (20,24,28,32).
Following this rule, the next second-layer difference will be:
32+4=36
Adding this to the last first-layer difference:
128+36=164
Finally, adding this to the last term of the main series:
Missing term=365+164=529
29−5=24
73−29=44
141−73=68
237−141=96
365−237=128
Now let's examine the differences of these differences (second layer of difference):
44−24=20
68−44=24
96−68=28
128−96=32
The second-layer differences increase by +4 each time (20,24,28,32).
Following this rule, the next second-layer difference will be:
32+4=36
Adding this to the last first-layer difference:
128+36=164
Finally, adding this to the last term of the main series:
Missing term=365+164=529