Type the next number in this sequence: 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 3 is +2, 3 to 7 is +4, 7 to 13 is +6, 13 to 21 is +8, and 21 to 31 is +10.Calculate Next Difference: Calculate the next difference to add to the last known term. The last increase was by 10 (from 21 to 31), so the next increase should be by 12.Add Calculated Difference: Add the calculated difference to the last known term to find the next number in the sequence. 31 + 12 = 43

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

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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

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 $3$ is $+2$ , $3$ to $7$ is $+4$ , $7$ to $13$ is $+6$ , $13$ to $3$ $0$ is $3$ $1$ , and $3$ $0$ to $3$ $3$ is $3$ $4$ .
Calculate Next Difference: Calculate the next difference to add to the last known term. $\newline$ The last increase was by $10$ (from $21$ to $31$ ), so the next increase should be by $12$ .
Add Calculated Difference: Add the calculated difference to the last known term to find the next number in the sequence. $31 + 12 = 43$