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

Pattern Analysis: To find the missing number in the sequence, we need to look for a pattern in the given numbers. Let's examine the differences between consecutive terms to see if there is a consistent pattern.Calculate Differences: The difference between the second and the first term is: 1 - 1 = 0Identify Increasing Pattern: The difference between the third and the second term is: 2 - 1 = 1Calculate Missing Number: The difference between the fourth and the third term is: 4 - 2 = 2Verify Calculation Error: Now, let's look at the differences between the terms after the missing number: 11 - (missing number) = difference 1 16 - 11 = 5, which is difference 2 22 - 16 = 6, which is difference 3It seems that the differences between consecutive terms are increasing by 1 each time. If we continue this pattern, the difference before the missing number (difference 0) should be 3, since the difference after it (difference 1) is 5.Let's calculate the missing number using the difference we expect (3): 4 + 3 = 7 So, the missing number should be 7.To verify, let's check if adding the next difference (5) to our found missing number (7) gives us the next term in the sequence (11): 7 + 5 = 12 This does not match the next term in the sequence, which is 11. This means there is a math error in our pattern assumption or calculation.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Type the missing number in this sequence: $\newline$ $1$ , $1$ , $2$ , $4$ , _____, $11$ , $16$ , $22$

View step-by-step help

Home

Math Problems

Grade 8

Sequences: mixed review

Full solution

Q. Type the missing number in this sequence:

\newline

1

1

2

4

, _____,

11

16

22

Pattern Analysis: To find the missing number in the sequence, we need to look for a pattern in the given numbers. Let's examine the differences between consecutive terms to see if there is a consistent pattern.
Calculate Differences: The difference between the second and the first term is: $1 - 1 = 0$
Identify Increasing Pattern: The difference between the third and the second term is: $2 - 1 = 1$
Calculate Missing Number: The difference between the fourth and the third term is: $4 - 2 = 2$
Verify Calculation Error: Now, let's look at the differences between the terms after the missing number: $\newline$ $11 - (\text{missing number}) = \text{difference 1}$ $\newline$ $16 - 11 = 5$ , which is $\text{difference 2}$ $\newline$ $22 - 16 = 6$ , which is $\text{difference 3}$
Verify Calculation Error: Now, let's look at the differences between the terms after the missing number: $\newline$ $11 - (\text{missing number}) = \text{difference } 1$ $\newline$ $16 - 11 = 5$ , which is difference $2$ $\newline$ $22 - 16 = 6$ , which is difference $3$ It seems that the differences between consecutive terms are increasing by $1$ each time. If we continue this pattern, the difference before the missing number (difference $0$ ) should be $3$ , since the difference after it (difference $1$ ) is $5$ .
Verify Calculation Error: Now, let's look at the differences between the terms after the missing number: $\newline$ $11 - (\text{missing number}) = \text{difference 1}$ $\newline$ $16 - 11 = 5$ , which is $\text{difference 2}$ $\newline$ $22 - 16 = 6$ , which is $\text{difference 3}$ It seems that the differences between consecutive terms are increasing by $1$ each time. If we continue this pattern, the difference before the missing number ( $\text{difference 0}$ ) should be $3$ , since the difference after it ( $\text{difference 1}$ ) is $5$ .Let's calculate the missing number using the difference we expect ( $3$ ): $\newline$ $16 - 11 = 5$ $1$ $\newline$ So, the missing number should be $16 - 11 = 5$ $2$ .
Verify Calculation Error: Now, let's look at the differences between the terms after the missing number: $\newline$ $11 - (\text{missing number}) = \text{difference 1}$ $\newline$ $16 - 11 = 5$ , which is $\text{difference 2}$ $\newline$ $22 - 16 = 6$ , which is $\text{difference 3}$ It seems that the differences between consecutive terms are increasing by $1$ each time. If we continue this pattern, the difference before the missing number ( $\text{difference 0}$ ) should be $3$ , since the difference after it ( $\text{difference 1}$ ) is $5$ .Let's calculate the missing number using the difference we expect ( $3$ ): $\newline$ $16 - 11 = 5$ $1$ $\newline$ So, the missing number should be $16 - 11 = 5$ $2$ .To verify, let's check if adding the next difference ( $5$ ) to our found missing number ( $16 - 11 = 5$ $2$ ) gives us the next term in the sequence ( $16 - 11 = 5$ $5$ ): $\newline$ $16 - 11 = 5$ $6$ $\newline$ This does not match the next term in the sequence, which is $16 - 11 = 5$ $5$ . This means there is a math error in our pattern assumption or calculation.