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

Identify Pattern in Sequence: We need to identify the pattern in the sequence. Let's look at the differences between consecutive terms: 0 to 0: difference of 0 0 to 1: difference of 1 1 to 3: difference of 2 3 to 6: difference of 3 6 to 10: difference of 4 It seems that the difference between each term is increasing by 1 each time.Find Next Difference: To find the next difference, we add 1 to the previous difference (which was 4): 4 + 1 = 5 So, the difference between the 6th term (10) and the next term should be 5.Add Difference to Last Term: Now, we add this difference to the last known term in the sequence to find the next term: 10 + 5 = 15 Therefore, the next number in the sequence should be 15.

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

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Math Problems

Grade 7

Sequences: mixed review

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Q. Type the next number in this sequence:

\newline

0

0

1

3

6

10

\_

Identify Pattern in Sequence: We need to identify the pattern in the sequence. Let's look at the differences between consecutive terms: $\newline$ $0$ to $0$ : difference of $0$ $\newline$ $0$ to $1$ : difference of $1$ $\newline$ $1$ to $3$ : difference of $2$ $\newline$ $3$ to $0$ $0$ : difference of $3$ $\newline$ $0$ $0$ to $0$ $3$ : difference of $0$ $4$ $\newline$ It seems that the difference between each term is increasing by $1$ each time.
Find Next Difference: To find the next difference, we add $1$ to the previous difference (which was $4$ ): $\newline$ $4 + 1 = 5$ $\newline$ So, the difference between the $6$ th term ( $10$ ) and the next term should be $5$ .
Add Difference to Last Term: Now, we add this difference to the last known term in the sequence to find the next term: $\newline$ $10 + 5 = 15$ $\newline$ Therefore, the next number in the sequence should be $15$ .