Question

What comes next in the series? 
\(2, 6, 12, 20, 30, \ ?\)

• A. 40
• B. 42
• C. 36
• D. 44

Hint:

Look at the difference between terms in a number series to detect patterns. Increasing or constant differences often indicate polynomial relationships.

Answer 1

The Correct Option is B

Solution:

To find the subsequent number in the sequence \(2, 6, 12, 20, 30, \ ?\), we first establish the pattern governing the sequence.

Let us analyze the increments between adjacent terms:

• Increment from \(2\) to \(6\): \(6 - 2 = 4\)
• Increment from \(6\) to \(12\): \(12 - 6 = 6\)
• Increment from \(12\) to \(20\): \(20 - 12 = 8\)
• Increment from \(20\) to \(30\): \(30 - 20 = 10\)

The sequence of increments is \(4, 6, 8, 10\). This pattern of increments increases by \(2\) with each step.

Following this established pattern, the next increment should be:

\(10 + 2 = 12\)

Therefore, the next term in the sequence is obtained by adding \(12\) to \(30\):

\(30 + 12 = 42\)

Consequently, the next number in the series is 42.