Question

Find out the appropriate next number in the series from the options below: 0, 2, 6, 12, 20, 30, 42, ?

• A. 56
• B. 62
• C. 49
• D. 5

Hint:

The differences between consecutive terms increase by 2 each time: 2, 4, 6, 8, 10, 12, then 14.

Answer 1

The Correct Option is A

Step 1: Find the difference between consecutive terms.
\(2-0=2\), \(6-2=4\), \(12-6=6\), \(20-12=8\), \(30-20=10\), \(42-30=12\).
Step 2: Observe the pattern in the differences.
The differences are 2, 4, 6, 8, 10, 12, which form an arithmetic sequence increasing by 2 each time.
Step 3: Find the next difference.
Continuing the pattern, the next difference after 12 is \(12 + 2 = 14\).
Step 4: Add this difference to the last term.
Next term \(= 42 + 14 = 56\).
Step 5: Rule out the other options.
Option 2 (62) would need a difference of 20, which breaks the pattern. Option 3 (49) and option 4 (5) do not fit the increasing-by-2 difference pattern at all. Only 56 fits.