Select the correct option that will fill in the blank and complete the series.
52, 56, 65, 81, 106, ?
- A132
- B140
- C142
- D122
Solution & Step-by-step Explanation
Let's look at the differences between consecutive terms:
56−52=4=2
2
65−56=9=3
2
81−65=16=4
2
106−81=25=5
2
The differences form a sequence of consecutive perfect squares (2
2
,3
2
,4
2
,5
2
).
The next difference must be 6
2
=36.
Therefore, the missing term is:
106+36=142
56−52=4=2
2
65−56=9=3
2
81−65=16=4
2
106−81=25=5
2
The differences form a sequence of consecutive perfect squares (2
2
,3
2
,4
2
,5
2
).
The next difference must be 6
2
=36.
Therefore, the missing term is:
106+36=142