Find the next number in the series: 2, 6, 12, 20, ... (2022)

Find the next number in the series: 2, 6, 12, 20, ... (2022)

Step 1: Look at the series of numbers: 2, 6, 12, 20.
Step 2: Identify the position of each number in the series: 2 is the 1st number, 6 is the 2nd, 12 is the 3rd, and 20 is the 4th.
Step 3: Notice that each number can be expressed using the formula n(n+1), where n is the position of the number in the series.
Step 4: Calculate the first four numbers using the formula: For n=1, 1(1+1) = 2; For n=2, 2(2+1) = 6; For n=3, 3(3+1) = 12; For n=4, 4(4+1) = 20.
Step 5: To find the next number, use n=5 in the formula: 5(5+1) = 5*6 = 30.
Step 6: Therefore, the next number in the series is 30.

Pattern Recognition – Identifying the underlying mathematical pattern in a sequence of numbers.
Quadratic Sequences – Understanding how to derive terms in a sequence based on polynomial expressions.