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

Identify Pattern: Identify the pattern in the sequence. Looking at the differences between the terms: 1-1=0, 3-1=2, 7-3=4, 13-7=6, 21-13=8. It seems that the difference between consecutive terms increases by 2 each time.Predict Next Difference: Predict the next difference in the sequence. If the pattern of increasing by 2 continues, the next difference should be 21-13=8, then 8+2=10.Calculate Next Number: Calculate the next number in the sequence. Add the predicted difference to the last known number in the sequence: 21+10=31.

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

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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

\_

Identify Pattern: Identify the pattern in the sequence. $\newline$ Looking at the differences between the terms: $1-1=0$ , $3-1=2$ , $7-3=4$ , $13-7=6$ , $21-13=8$ . It seems that the difference between consecutive terms increases by $2$ each time.
Predict Next Difference: Predict the next difference in the sequence. $\newline$ If the pattern of increasing by $2$ continues, the next difference should be $21-13=8$ , then $8+2=10$ .
Calculate Next Number: Calculate the next number in the sequence. $\newline$ Add the predicted difference to the last known number in the sequence: $21+10=31$ .