Type the next number in this sequence: 1, 1, 3, 7, 13, 21, 31, _____

Identify Pattern: Identify the pattern in the sequence. We notice that the difference between consecutive terms is increasing by 2 each time. 1 to 1: difference of 0 (1 + 0 = 1) 1 to 3: difference of 2 (1 + 2 = 3) 3 to 7: difference of 4 (3 + 4 = 7) 7 to 13: difference of 6 (7 + 6 = 13) 13 to 21: difference of 8 (13 + 8 = 21) 21 to 31: difference of 10 (21 + 10 = 31)Calculate Next Difference: Calculate the next difference in the sequence. The last difference we calculated was 10, so the next difference should be 10 + 2 = 12.Find Next Number: Add the next difference to the last term in the sequence to find the next number. 31 + 12 = 43

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Type the next number in this sequence: $\newline$ $1$ , $1$ , $3$ , $7$ , $13$ , $21$ , $31$ , $\_$

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Math Problems

Algebra 1

Sequences: mixed review

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Q. Type the next number in this sequence:

\newline

1

1

3

7

13

21

31

\_

Identify Pattern: Identify the pattern in the sequence. $\newline$ We notice that the difference between consecutive terms is increasing by $2$ each time. $\newline$ $1$ to $1$ : difference of $0$ ( $1 + 0 = 1$ ) $\newline$ $1$ to $3$ : difference of $2$ ( $1 + 2 = 3$ ) $\newline$ $3$ to $7$ : difference of $1$ $0$ ( $1$ $1$ ) $\newline$ $7$ to $1$ $3$ : difference of $1$ $4$ ( $1$ $5$ ) $\newline$ $1$ $3$ to $1$ $7$ : difference of $1$ $8$ ( $1$ $9$ ) $\newline$ $1$ $7$ to $0$ $1$ : difference of $0$ $2$ ( $0$ $3$ )
Calculate Next Difference: Calculate the next difference in the sequence. $\newline$ The last difference we calculated was $10$ , so the next difference should be $10 + 2 = 12$ .
Find Next Number: Add the next difference to the last term in the sequence to find the next number. $31 + 12 = 43$