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 determine the next number in the series \(2, 6, 12, 20, 30, \ ?\), we first identify the pattern in the sequence.

Let's examine the differences between consecutive terms:

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

The differences between the terms are \(4, 6, 8, 10\). This sequence of differences is increasing by \(2\) each time.

Continuing this pattern, the next difference should be:

\(10 + 2 = 12\)

Thus, the next term in the series can be found by adding \(12\) to \(30\):

\(30 + 12 = 42\)

Hence, the next number in the series is 42.

Answer 2

Step 1: Observe the pattern in the series.
Let's examine the difference between consecutive terms: \[ 6 - 2 = 4, 12 - 6 = 6, 20 - 12 = 8, 30 - 20 = 10 \] So the differences are increasing by 2 each time: \(+4, +6, +8, +10\) 
Step 2: Add the next difference (which should be +12) to the last term: \[ 30 + 12 = 42 \]