Type the next number in this sequence: 1, 2, 4, 7, 11, 16, 22, _____

Identify Pattern: To find the pattern, let's look at the differences between consecutive numbers in the sequence. 2 - 1 = 1 4 - 2 = 2 7 - 4 = 3 11 - 7 = 4 16 - 11 = 5 22 - 16 = 6 It seems that the difference between each number and the one before it increases by 1 each time.Predict Next Number: If the pattern continues, the difference between the next number and 22 should be 7, since the last difference was 6. So, we add 7 to 22 to find the next number in the sequence. 22 + 7 = 29Verify Pattern: We check the pattern to ensure that the differences are indeed increasing by 1 each time. 1, 2, 4, 7, 11, 16, 22, 29 The differences are: 1, 2, 3, 4, 5, 6, 7 The pattern holds true, so there is no math error.

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Type the next number in this sequence: $\newline$ $1$ , $2$ , $4$ , $7$ , $11$ , $16$ , $22$ , $\_$

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Math Problems

Grade 8

Sequences: mixed review

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Q. Type the next number in this sequence:

\newline

1

2

4

7

11

16

22

\_

Identify Pattern: To find the pattern, let's look at the differences between consecutive numbers in the sequence. $\newline$ $2 - 1 = 1$ $\newline$ $4 - 2 = 2$ $\newline$ $7 - 4 = 3$ $\newline$ $11 - 7 = 4$ $\newline$ $16 - 11 = 5$ $\newline$ $22 - 16 = 6$ $\newline$ It seems that the difference between each number and the one before it increases by $1$ each time.
Predict Next Number: If the pattern continues, the difference between the next number and $22$ should be $7$ , since the last difference was $6$ . So, we add $7$ to $22$ to find the next number in the sequence. $22 + 7 = 29$
Verify Pattern: We check the pattern to ensure that the differences are indeed increasing by $1$ each time. $1, 2, 4, 7, 11, 16, 22, 29$ The differences are: $1, 2, 3, 4, 5, 6, 7$ The pattern holds true, so there is no math error.