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Type the missing number in this sequence: $\newline$ $4$ , $6$ , $\_$ , $13$ , $18$ , $24$ , $31$ , $39$

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Sequences: mixed review

Full solution

Q. Type the missing number in this sequence:

\newline

4

,

6

,

\_

,

13

,

18

,

24

,

31

,

39

Find Pattern in Sequence: Let's look for a pattern in the sequence. We will start by finding the differences between consecutive terms.
Calculate Differences: The difference between the second term $6$ and the first term $4$ is $2$ $6 - 4 = 2$ .
Analyze Differences: Now, let's find the difference between the fourth term $13$ and the second term $6$ , which is $7$ $13 - 6 = 7$ .
Identify Pattern in Differences: We notice that the difference between the terms is not consistent, so let's check the differences between the other terms to see if there is another pattern.
Identify Pattern in Differences: We notice that the difference between the terms is not consistent, so let's check the differences between the other terms to see if there is another pattern.The difference between the fifth term ( $18$ ) and the fourth term ( $13$ ) is $5$ ( $18 - 13 = 5$ ).
Identify Pattern in Differences: We notice that the difference between the terms is not consistent, so let's check the differences between the other terms to see if there is another pattern.The difference between the fifth term ( $18$ ) and the fourth term ( $13$ ) is $5$ ( $18 - 13 = 5$ ).The difference between the sixth term ( $24$ ) and the fifth term ( $18$ ) is $6$ ( $24 - 18 = 6$ ).
Identify Pattern in Differences: We notice that the difference between the terms is not consistent, so let's check the differences between the other terms to see if there is another pattern.The difference between the fifth term ( $18$ ) and the fourth term ( $13$ ) is $5$ ( $18 - 13 = 5$ ).The difference between the sixth term ( $24$ ) and the fifth term ( $18$ ) is $6$ ( $24 - 18 = 6$ ).The difference between the seventh term ( $31$ ) and the sixth term ( $24$ ) is $13$ $0$ ( $13$ $1$ ).
Identify Pattern in Differences: We notice that the difference between the terms is not consistent, so let's check the differences between the other terms to see if there is another pattern.The difference between the fifth term ( $18$ ) and the fourth term ( $13$ ) is $5$ ( $18 - 13 = 5$ ).The difference between the sixth term ( $24$ ) and the fifth term ( $18$ ) is $6$ ( $24 - 18 = 6$ ).The difference between the seventh term ( $31$ ) and the sixth term ( $24$ ) is $13$ $0$ ( $13$ $1$ ).The difference between the eighth term ( $13$ $2$ ) and the seventh term ( $31$ ) is $13$ $4$ ( $13$ $5$ ).
Identify Pattern in Differences: We notice that the difference between the terms is not consistent, so let's check the differences between the other terms to see if there is another pattern.The difference between the fifth term ( $18$ ) and the fourth term ( $13$ ) is $5$ ( $18 - 13 = 5$ ).The difference between the sixth term ( $24$ ) and the fifth term ( $18$ ) is $6$ ( $24 - 18 = 6$ ).The difference between the seventh term ( $31$ ) and the sixth term ( $24$ ) is $13$ $0$ ( $13$ $1$ ).The difference between the eighth term ( $13$ $2$ ) and the seventh term ( $31$ ) is $13$ $4$ ( $13$ $5$ ).We can see a pattern in the differences: $13$ $6$ . It seems that the differences are not increasing by a constant amount, but let's check the differences between the differences.
Identify Pattern in Differences: We notice that the difference between the terms is not consistent, so let's check the differences between the other terms to see if there is another pattern.The difference between the fifth term ( $18$ ) and the fourth term ( $13$ ) is $5$ ( $18 - 13 = 5$ ).The difference between the sixth term ( $24$ ) and the fifth term ( $18$ ) is $6$ ( $24 - 18 = 6$ ).The difference between the seventh term ( $31$ ) and the sixth term ( $24$ ) is $13$ $0$ ( $13$ $1$ ).The difference between the eighth term ( $13$ $2$ ) and the seventh term ( $31$ ) is $13$ $4$ ( $13$ $5$ ).We can see a pattern in the differences: $13$ $6$ . It seems that the differences are not increasing by a constant amount, but let's check the differences between the differences.The difference between $5$ and $13$ $8$ is $13$ $9$ ( $5$ $0$ ), and the difference between $6$ and $5$ is $5$ $3$ ( $5$ $4$ ). This does not seem to follow a simple pattern, so we may have made a mistake. Let's re-evaluate the differences between the terms.

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

\newline

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\newline

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