Type the next number in this sequence: 2, 3, 6, 11, 18, _____

Identify Pattern: Identify the pattern in the sequence. We notice that the difference between consecutive terms is increasing by one each time. 2 to 3 is an increase of 1. 3 to 6 is an increase of 3. 6 to 11 is an increase of 5. 11 to 18 is an increase of 7.Predict Next Difference: Predict the next difference in the sequence. Since the differences are increasing by 2 each time (1, 3, 5, 7), the next difference should be 7 + 2 = 9.Add Predicted Difference: Add the predicted difference to the last known term in the sequence to find the next term. 18 + 9 = 27Verify Pattern: Verify the pattern with the new term. The sequence with the new term is 2, 3, 6, 11, 18, 27. The differences between the terms are now 1, 3, 5, 7, 9, which confirms our pattern.

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Type the next number in this sequence: $\newline$ $2$ , $3$ , $6$ , $11$ , $18$ , $\_\_\_\_$

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Math Problems

Algebra 1

Sequences: mixed review

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Q. Type the next number in this sequence:

\newline

2

3

6

11

18

\_\_\_\_

Identify Pattern: Identify the pattern in the sequence. $\newline$ We notice that the difference between consecutive terms is increasing by one each time. $\newline$ $2$ to $3$ is an increase of $1$ . $\newline$ $3$ to $6$ is an increase of $3$ . $\newline$ $6$ to $11$ is an increase of $5$ . $\newline$ $11$ to $3$ $0$ is an increase of $3$ $1$ .
Predict Next Difference: Predict the next difference in the sequence. $\newline$ Since the differences are increasing by $2$ each time ( $1$ , $3$ , $5$ , $7$ ), the next difference should be $7 + 2 = 9$ .
Add Predicted Difference: Add the predicted difference to the last known term in the sequence to find the next term. $18 + 9 = 27$
Verify Pattern: Verify the pattern with the new term. $\newline$ The sequence with the new term is $2, 3, 6, 11, 18, 27$ . $\newline$ The differences between the terms are now $1, 3, 5, 7, 9$ , which confirms our pattern.