These are triangular numbers formed by adding consecutive natural numbers: 1, 1+2 = 3, 1+2+3 = 6, 1+2+3+4 = 10 and 1+2+3+4+5 = 15. The next triangular number is 1+2+3+4+5+6 = 21. Therefore, 21 is the correct next term.
Option A:
Option A is 16, which does not arise from summing the first 6 natural numbers. It is only one more than 15 and ignores the triangular pattern. Hence, it is not correct.
Option B:
Option B is 18, which is between 15 and 21 but not equal to the next triangular value. Including 18 would make the pattern unclear. Therefore, this option is unsuitable.
Option C:
Option C equals 21, which is the sum of the first 6 positive integers and matches the known triangular number T₆. The series 1, 3, 6, 10, 15, 21 stays consistent with this definition. Thus, 21 is the valid continuation.
Option D:
Option D is 24, which is not a triangular number at this position. While 24 has other mathematical roles, it does not fit the specific summation pattern here. So, it cannot be chosen.
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