What is the next number in the following series: 1, 3, 6, 10, 15, 21,...?

To determine the next number in the series 1, 3, 6, 10, 15, 21, we first identify the pattern in the sequence. Each number in the series corresponds to the sum of the first ( n ) natural numbers, where ( n ) represents the position in the sequence.

• The first number, 1, can be viewed as ( 1 ) (the sum of the first 1 number).

• The second number, 3, is ( 1 + 2 ) (the sum of the first 2 numbers).

• The third number, 6, is ( 1 + 2 + 3 ) (the sum of the first 3 numbers).

• Continuing this way, we find:

• 10 = 1 + 2 + 3 + 4

• 15 = 1 + 2 + 3 + 4 + 5

• 21 = 1 + 2 + 3 + 4 + 5 + 6

Thus, to find the next number in the series, we add the next integer (7) to the last number (21):

21 + 7 =