The sequence 1, 3, 6, 10, ldots is | vedclass

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(D) To determine the nature of the sequence $1, 3, 6, 10, \ldots$,let us examine the differences between consecutive terms:$3 - 1 = 2$$6 - 3 = 3$$10 -

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the sequence of triangular numbers

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(D) To determine the nature of the sequence $1, 3, 6, 10, \ldots$,let us examine the differences between consecutive terms:$3 - 1 = 2$$6 - 3 = 3$$10 - 6 = 4$The differences are $2, 3, 4, \ldots$,which are not constant,so it is not an arithmetic progression.The ratios are $3/1 = 3$,$6/3 = 2$,$10/6 = 1.66$,which are not constant,so it is not a geometric progression.The Fibonacci sequence is defined by $F_n = F_{n-1} + F_{n-2}$,which does not match this pattern.These numbers are known as triangular numbers,defined by the formula $T_n = \frac{n(n+1)}{2}$.For $n=1, T_1 = 1$; for $n=2, T_2 = 3$; for $n=3, T_3 = 6$; for $n=4, T_4 = 10$. Thus,it is the sequence of triangular numbers.

The sequence $1, 3, 6, 10, \ldots$ is

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