Complete the pattern: 2, 12, 36, 80, 150, ?
A246
B240
C252
D258
Answer:
C. 252
Read Explanation:
Pattern Analysis
- The given sequence is 2, 12, 36, 80, 150, ?.
- To find the pattern, let us express each term using the formula n³ + n² or n²(n+1):
- For n=1: 1³ + 1² = 1 + 1 = 2
- For n=2: 2³ + 2² = 8 + 4 = 12
- For n=3: 3³ + 3² = 27 + 9 = 36
- For n=4: 4³ + 4² = 64 + 16 = 80
- For n=5: 5³ + 5² = 125 + 25 = 150
- Following this logical progression, the next term (n=6) is:
- 6³ + 6² = 216 + 36 = 252
Alternative Method: Difference Analysis
- Analyze the differences between consecutive terms:
- 12 - 2 = 10
- 36 - 12 = 24
- 80 - 36 = 44
- 150 - 80 = 70
- Now, analyze the second level of differences:
- 24 - 10 = 14
- 44 - 24 = 20
- 70 - 44 = 26
- The differences in the second level are increasing by 6 (14, 20, 26).
- The next second-level difference will be 26 + 6 = 32.
- The next first-level difference will be 70 + 32 = 102.
- The final term is 150 + 102 = 252.