Type the missing number in this sequence: 2, 2, 4, _____, 14, 22, 32

Identify Pattern: Step 1: Identify the pattern in the sequence. Looking at the sequence: 2, 2, 4, _____, 14, 22, 32. We need to find the difference between consecutive terms to see if there's a pattern. Difference between 2 and 2 is 0. Difference between 2 and 4 is 2. We need to find the next difference that makes sense with the rest of the sequence.Find Differences: Step 2: Continue finding differences and predict the next term. Difference between 4 and the next term (let's call it x) should follow a pattern that fits with the differences between the later terms: Difference between x and 14, 14 and 22, and 22 and 32 are 8, 8, and 10 respectively. Assuming a linear increase, the difference before 8 could be 6 (since 8 - 2 = 6). So, 4 + 6 = 10.Verify Prediction: Step 3: Verify the pattern. If x = 10, then the sequence is 2, 2, 4, 10, 14, 22, 32. Difference between 10 and 14 is 4, but we expected 8; this doesn't match our prediction.

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Type the missing number in this sequence: $\newline$ $2$ , $2$ , $4$ , _____, $14$ , $22$ , $32$

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Math Problems

Grade 8

Sequences: mixed review

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Q. Type the missing number in this sequence:

\newline

2

2

4

, _____,

14

22

32

Identify Pattern: Step $1$ : Identify the pattern in the sequence. $\newline$ Looking at the sequence: $2, 2, 4, \_\_\_\_, 14, 22, 32$ . We need to find the difference between consecutive terms to see if there's a pattern. $\newline$ Difference between $2$ and $2$ is $0$ . $\newline$ Difference between $2$ and $4$ is $2$ . $\newline$ We need to find the next difference that makes sense with the rest of the sequence.
Find Differences: Step $2$ : Continue finding differences and predict the next term. $\newline$ Difference between $4$ and the next term (let's call it $x$ ) should follow a pattern that fits with the differences between the later terms: $\newline$ Difference between $x$ and $14$ , $14$ and $22$ , and $22$ and $32$ are $8$ , $8$ , and $x$ $0$ respectively. $\newline$ Assuming a linear increase, the difference before $8$ could be $x$ $2$ (since $x$ $3$ ). $\newline$ So, $x$ $4$ .
Verify Prediction: Step $3$ : Verify the pattern. $\newline$ If $x = 10$ , then the sequence is $2, 2, 4, 10, 14, 22, 32$ . $\newline$ Difference between $10$ and $14$ is $4$ , but we expected $8$ ; this doesn't match our prediction.