Type the missing number in this sequence: 3, 4, 7, 12, 19, _____, 39, 52

Identify Pattern: Identify the pattern in the sequence. We need to determine how each number in the sequence is related to the previous numbers.Analyze Differences: Analyze the differences between consecutive terms. The difference between 4 and 3 is 1. The difference between 7 and 4 is 3. The difference between 12 and 7 is 5. The difference between 19 and 12 is 7. It seems that 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 7 + 2 = 9.Calculate Missing Number: Calculate the missing number. Add the predicted difference to the last known number in the sequence. 19 + 9 = 28Verify Pattern Continues: Verify the pattern continues after the missing number. The difference between 39 and the missing number should be 11, since we are adding 2 to the previous difference of 9. 28 + 11 = 39, which is correct.Confirm with Next Difference: Confirm the pattern with the next difference. The difference between 52 and 39 is 13, which is 2 more than the previous difference of 11. 39 + 13 = 52, which is correct.

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Type the missing number in this sequence: $\newline$ $3,\;4,\;7,\;12,\;19,\;\_\_\_\_,\;39,\;52$

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Algebra 1

Sequences: mixed review

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Q. Type the missing number in this sequence:

\newline

3,\;4,\;7,\;12,\;19,\;\_\_\_\_,\;39,\;52

Identify Pattern: Identify the pattern in the sequence. $\newline$ We need to determine how each number in the sequence is related to the previous numbers.
Analyze Differences: Analyze the differences between consecutive terms. $\newline$ The difference between $4$ and $3$ is $1$ . $\newline$ The difference between $7$ and $4$ is $3$ . $\newline$ The difference between $12$ and $7$ is $5$ . $\newline$ The difference between $19$ and $12$ is $7$ . $\newline$ It seems that the differences are increasing by $3$ $2$ each time.
Predict Next Difference: Predict the next difference in the pattern. $\newline$ If the pattern of differences continues, the next difference should be $7 + 2 = 9$ .
Calculate Missing Number: Calculate the missing number. $\newline$ Add the predicted difference to the last known number in the sequence. $\newline$ $19 + 9 = 28$
Verify Pattern Continues: Verify the pattern continues after the missing number. $\newline$ The difference between $39$ and the missing number should be $11$ , since we are adding $2$ to the previous difference of $9$ . $\newline$ $28 + 11 = 39$ , which is correct.
Confirm with Next Difference: Confirm the pattern with the next difference. $\newline$ The difference between $52$ and $39$ is $13$ , which is $2$ more than the previous difference of $11$ . $\newline$ $39 + 13 = 52$ , which is correct.