In the following question, select the missing number from the given series.
56, 65, 81, 106, ?, 191
- A142
- B164
- C138
- D154
Solution & Step-by-step Explanation
Let's find the differences between the consecutive numbers:
65−56=9=3
2
81−65=16=4
2
106−81=25=5
2
The pattern shows that the differences are squares of consecutive natural numbers starting from 3:
3
2
,4
2
,5
2
,6
2
,7
2
,…
Following the pattern, the next difference must be 6
2
=36:
Missing number=106+36=142
Let's cross-check for the next term:
142+7
2
=142+49=191
This is perfectly consistent.
65−56=9=3
2
81−65=16=4
2
106−81=25=5
2
The pattern shows that the differences are squares of consecutive natural numbers starting from 3:
3
2
,4
2
,5
2
,6
2
,7
2
,…
Following the pattern, the next difference must be 6
2
=36:
Missing number=106+36=142
Let's cross-check for the next term:
142+7
2
=142+49=191
This is perfectly consistent.