Type the next number in this sequence: 1, 1, 3, 7, 13, _____

Identify Pattern: Identify the pattern in the sequence. We need to look at the differences between consecutive terms to see if there is a recognizable pattern. 1 to 1: Difference is 0 1 to 3: Difference is 2 3 to 7: Difference is 4 7 to 13: Difference is 6 It seems that the difference between each term is increasing by 2 each time.Apply Pattern: Apply the pattern to find the next difference. If the pattern of differences continues, the next difference should be 2 more than the previous difference, which was 6. 6 (previous difference) + 2 = 8 (next difference)Find Next Number: Add the next difference to the last term in the sequence to find the next number. The last term in the sequence is 13, so we add the next difference, which is 8, to 13. 13 + 8 = 21

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Type the next number in this sequence: $\newline$ $1$ , $1$ , $3$ , $7$ , $13$ , $\_$

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Math Problems

Grade 7

Sequences: mixed review

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Q. Type the next number in this sequence:

\newline

1

1

3

7

13

\_

Identify Pattern: Identify the pattern in the sequence. $\newline$ We need to look at the differences between consecutive terms to see if there is a recognizable pattern. $\newline$ $1$ to $1$ : Difference is $0$ $\newline$ $1$ to $3$ : Difference is $2$ $\newline$ $3$ to $7$ : Difference is $4$ $\newline$ $7$ to $1$ $0$ : Difference is $1$ $1$ $\newline$ It seems that the difference between each term is increasing by $2$ each time.
Apply Pattern: Apply the pattern to find the next difference. $\newline$ If the pattern of differences continues, the next difference should be $2$ more than the previous difference, which was $6$ . $\newline$ $6$ (previous difference) + $2$ = $8$ (next difference)
Find Next Number: Add the next difference to the last term in the sequence to find the next number. $\newline$ The last term in the sequence is $13$ , so we add the next difference, which is $8$ , to $13$ . $\newline$ $13 + 8 = 21$