Complete the series.
2, 6, 12, 20, 30, 42, _____
- A65
- B56
- C49
- D51
Solution & Step-by-step Explanation
Let's analyze the difference between consecutive terms in the series:
6−2=4
12−6=6
12=8
30−20=10
42−30=12
The differences form an arithmetic sequence: +4,+6,+8,+10,+12.
Following this established progression, the next difference must be +14.
Adding 14 to the last term:
42+14=56
Alternative Logic:
The sequence can also be written in the form n
2
+n:
1
2
+1=2
2
2
+2=6
3
2
+3=12
4
2
+4=20
5
2
+5=30
6
2
+6=42
7
2
+7=49+7=56
6−2=4
12−6=6
12=8
30−20=10
42−30=12
The differences form an arithmetic sequence: +4,+6,+8,+10,+12.
Following this established progression, the next difference must be +14.
Adding 14 to the last term:
42+14=56
Alternative Logic:
The sequence can also be written in the form n
2
+n:
1
2
+1=2
2
2
+2=6
3
2
+3=12
4
2
+4=20
5
2
+5=30
6
2
+6=42
7
2
+7=49+7=56