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

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Sequences: mixed review

Full solution

Q. Type the next number in this sequence:

\newline

0

,

0

,

1

,

3

,

6

,

10

,

15

,

\_

Identify Pattern: Identify the pattern in the sequence. $\newline$ The sequence appears to be increasing by consecutive integers: $0$ $(0+0)$ , $0$ $(0+1)$ , $1$ $(1+1)$ , $3$ $(2+1)$ , $6$ $(3+1)$ , $(0+0)$ $0$ $(0+0)$ $1$ , $(0+0)$ $2$ $(0+0)$ $3$ . $\newline$ Pattern: Each term after the first is the sum of the previous term and the next integer in the counting sequence.
Determine Differences: Determine the difference between consecutive terms. $\newline$ $0$ to $0$ : $+0$ $\newline$ $0$ to $1$ : $+1$ $\newline$ $1$ to $3$ : $+2$ $\newline$ $3$ to $0$ $0$ : $0$ $1$ $\newline$ $0$ $0$ to $0$ $3$ : $0$ $4$ $\newline$ $0$ $3$ to $0$ $6$ : $0$ $7$ $\newline$ The differences are consecutive integers starting from $0$ .
Find Next Difference: Find the next difference to add to the last term in the sequence. $\newline$ The last difference was $+5$ , so the next difference should be $+6$ .
Calculate Next Term: Calculate the next term in the sequence. $\newline$ Add the next difference to the last term: $15 + 6 = 21$ .

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

\newline

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\newline

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