Type the next number in this sequence: 0, 1, 3, 6, 10, 15, 21, _____

Identify Pattern: Identify the pattern in the sequence. Each number appears to be the sum of all natural numbers up to a certain point, which is known as the triangular number sequence. Calculation: 0 = 0, 1 = 1, 3 = 1+2, 6 = 1+2+3, 10 = 1+2+3+4, 15 = 1+2+3+4+5, 21 = 1+2+3+4+5+6.Determine Next Position: Determine the next position in the sequence. The sequence's positions are increasing by 1 each time: 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, ... The next position is the 8th.Calculate 8th Triangular Number: Calculate the 8th triangular number. Using the formula for the nth triangular number, T_n = n(n+1)/2, where n is the position in the sequence. Calculation: T_8 = 8(8+1)/2 = 8*9/2 = 36.

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Type the next number in this sequence: $\newline$ $0$ , $1$ , $3$ , $6$ , $10$ , $15$ , $21$ , $\_$

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Math Problems

Algebra 2

Sequences: mixed review

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Q. Type the next number in this sequence:

\newline

0

1

3

6

10

15

21

\_

Identify Pattern: Identify the pattern in the sequence. $\newline$ Each number appears to be the sum of all natural numbers up to a certain point, which is known as the triangular number sequence. $\newline$ Calculation: $0 = 0$ , $1 = 1$ , $3 = 1+2$ , $6 = 1+2+3$ , $10 = 1+2+3+4$ , $15 = 1+2+3+4+5$ , $21 = 1+2+3+4+5+6$ .
Determine Next Position: Determine the next position in the sequence. $\newline$ The sequence's positions are increasing by $1$ each time: $1$ st, $2$ nd, $3$ rd, $4$ th, $5$ th, $6$ th, $7$ th, ... $\newline$ The next position is the $8$ th.
Calculate $8$ th Triangular Number: Calculate the $8$ th triangular number. $\newline$ Using the formula for the nth triangular number, $T_n = \frac{n(n+1)}{2}$ , where $n$ is the position in the sequence. $\newline$ Calculation: $T_8 = \frac{8(8+1)}{2} = \frac{8\times9}{2} = 36$ .