Type the missing number in this sequence: 1, 2, 5, 10, _____, 26, 37

Identify Pattern: Identify the pattern in the sequence. We need to look at the differences between the numbers to see if there is a consistent pattern. Difference between 2 and 1 is 1. Difference between 5 and 2 is 3. Difference between 10 and 5 is 5. It seems like the differences are increasing by 2 each time.Predict Next Difference: Predict the next difference in the pattern. If the pattern of differences continues, the next difference should be 5 + 2 = 7.Use Predicted Difference: Use the predicted difference to find the missing number. The missing number should be 10 + 7 = 17.Verify Pattern Continues: Verify the pattern continues after the missing number. If 17 is the correct number, the difference between the next number (26) and 17 should be 9, which is 2 more than the last difference we used (7). 26 - 17 = 9, which fits the pattern.Confirm Last Two Numbers: Confirm the pattern holds for the last two numbers in the sequence. The difference between 37 and 26 should be 11, which is 2 more than the previous difference (9). 37 - 26 = 11, which fits the pattern.

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Type the missing number in this sequence: $\newline$ $1$ , $2$ , $5$ , $10$ , $\_$ , $26$ , $37$

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Math Problems

Grade 8

Sequences: mixed review

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Q. Type the missing number in this sequence:

\newline

1

2

5

10

\_

26

37

Identify Pattern: Identify the pattern in the sequence. $\newline$ We need to look at the differences between the numbers to see if there is a consistent pattern. $\newline$ Difference between $2$ and $1$ is $1$ . $\newline$ Difference between $5$ and $2$ is $3$ . $\newline$ Difference between $10$ and $5$ is $5$ . $\newline$ It seems like the differences are increasing by $2$ each time.
Predict Next Difference: Predict the next difference in the pattern. $\newline$ If the pattern of differences continues, the next difference should be $5 + 2 = 7$ .
Use Predicted Difference: Use the predicted difference to find the missing number. The missing number should be $10 + 7 = 17$ .
Verify Pattern Continues: Verify the pattern continues after the missing number. $\newline$ If $17$ is the correct number, the difference between the next number ( $26$ ) and $17$ should be $9$ , which is $2$ more than the last difference we used ( $7$ ). $\newline$ $26 - 17 = 9$ , which fits the pattern.
Confirm Last Two Numbers: Confirm the pattern holds for the last two numbers in the sequence. $\newline$ The difference between $37$ and $26$ should be $11$ , which is $2$ more than the previous difference ( $9$ ). $\newline$ $37 - 26 = 11$ , which fits the pattern.