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Type the next number in this sequence: $\newline$ $2$ , $4$ , $7$ , $11$ , $16$ , $22$ , $29$ , $\_$

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Sequences: mixed review

Full solution

Q. Type the next number in this sequence:

\newline

2

,

4

,

7

,

11

,

16

,

22

,

29

,

\_

Identify Differences: To find the pattern, let's look at the differences between consecutive numbers in the sequence. $\newline$ Difference between $4$ and $2$ is $2$ . $\newline$ Difference between $7$ and $4$ is $3$ . $\newline$ Difference between $11$ and $7$ is $4$ . $\newline$ Difference between $16$ and $11$ is $2$ $1$ . $\newline$ Difference between $2$ $2$ and $16$ is $2$ $4$ . $\newline$ Difference between $2$ $5$ and $2$ $2$ is $7$ . $\newline$ It seems that with each step, the difference increases by $2$ $8$ .
Calculate Next Number: Now, to find the next number, we add $8$ to the last number in the sequence (since the last difference was $7$ , the next difference should be $8$ ). $\newline$ $29 + 8 = 37$
Verify Pattern: We check the pattern to ensure that the difference between the numbers we have found continues to increase by $1$ . The difference between $37$ and $29$ is indeed $8$ , which is $1$ more than the previous difference of $7$ .

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\newline

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