The given sequence is triangular numbers, where each term is the sum of the first ( n ) positive integers.
Pattern Analysis
- Term 1: ( 1 = 1 )
- Term 2: ( 3 = 1 + 2 )
- Term 3: ( 6 = 1 + 2 + 3 )
- Term 4: ( 10 = 1 + 2 + 3 + 4 )
- Term 5: ( 15 = 1 + 2 + 3 + 4 + 5 )
General Formula
The ( n )-th term ( T(n) ) of the sequence is the sum of the first ( n ) integers:
[ T(n) = \frac{n(n+1)}{2} ]
Next Term (Term 6)
Using the formula:
[ T(6) = \frac{6(6+1)}{2} = \frac{6×7}{2} = 21 ]
Answer: The next term is 21, and the general formula is ( \frac{n(n+1)}{2} ).
If you needed the next term specifically: (\boxed{21})
If you needed the formula: (\boxed{\frac{n(n+1)}{2}})
(Assuming the question asks for the next term, the most likely answer is (\boxed{21}).)
(\boxed{21})
作者声明:本文包含人工智能生成内容。
