Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
What should come in place of ‘?’ in the given series? 2, 6, 12, 20, 30, ?
40
42
44
46
42
Observe the constant second-level difference or the n squared plus n pattern (n² + n).
Observe the constant second-level difference or the n squared plus n pattern (n² + n).
Analyze the pattern of differences
Find the difference between consecutive terms: 6-2=4, 12-6=6, 20-12=8, 30-20=10. The differences follow an arithmetic progression of consecutive even numbers: 4, 6, 8, 10.
Predict the next difference and term
The next even number in the sequence after 10 is 12. Adding this to the last term: 30 + 12 = 42.
Alternative Verification
The series follows the formula n² + n where n starts from 1: (1²⁺¹)=2, (2²⁺²)=6, (3²⁺³)=12, (4²⁺⁴)=20, (5²⁺⁵)=30. Therefore, the next term is (6²⁺⁶) = 36 + 6 = 42.
A: 40 is incorrect as it assumes a constant difference of 10, C: 44 is incorrect as it follows a logic of adding 14 instead of 12, D: 46 is incorrect as it would require a difference of 16.
B is correct because the series follows an increment pattern of consecutive even numbers (+4, +6, +8, +10, +12), leading to 30 + 12 = 42.
For any increasing series, always check the difference of differences (second-level difference); it reveals linear patterns in otherwise complex-looking series.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download • 100K+ Aspirants