Type the missing number in this sequence: 1, _____, 7, 13, 21, 31, 43, 57

Identify Pattern: Identify the pattern in the sequence. We will look at the differences between consecutive terms to see if there is a pattern.Calculate Differences: Calculate the differences between consecutive terms that are given. 7 - 1 = 6 13 - 7 = 6 21 - 13 = 8 31 - 21 = 10 43 - 31 = 12 57 - 43 = 14 It seems that the difference between consecutive terms is increasing by 2 each time.Determine Missing Number: Determine the difference between the first and the missing term. Since the difference starts at 6 and increases by 2, the difference before 6 should be 4.Calculate Missing Number: Calculate the missing number using the difference found in the previous step. 1 + 4 = 5 The missing number should be 5.Verify Pattern: Verify the pattern by checking if the sequence is correct with the missing number filled in. 1, 5, 7, 13, 21, 31, 43, 57 Check the differences again: 5 - 1 = 4 7 - 5 = 2 13 - 7 = 6 21 - 13 = 8 31 - 21 = 10 43 - 31 = 12 57 - 43 = 14 The pattern of differences (4, 2, 6, 8, 10, 12, 14) does not increase by 2 each time, which means there is a mistake.

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Type the missing number in this sequence: $\newline$ $1$ , _____, $7$ , $13$ , $21$ , $31$ , $43$ , $57$

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Algebra 1

Sequences: mixed review

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Q. Type the missing number in this sequence:

\newline

1

, _____,

7

13

21

31

43

57

Identify Pattern: Identify the pattern in the sequence. $\newline$ We will look at the differences between consecutive terms to see if there is a pattern.
Calculate Differences: Calculate the differences between consecutive terms that are given. $\newline$ $7 - 1 = 6$ $\newline$ $13 - 7 = 6$ $\newline$ $21 - 13 = 8$ $\newline$ $31 - 21 = 10$ $\newline$ $43 - 31 = 12$ $\newline$ $57 - 43 = 14$ $\newline$ It seems that the difference between consecutive terms is increasing by $2$ each time.
Determine Missing Number: Determine the difference between the first and the missing term. $\newline$ Since the difference starts at $6$ and increases by $2$ , the difference before $6$ should be $4$ .
Calculate Missing Number: Calculate the missing number using the difference found in the previous step. $\newline$ $1 + 4 = 5$ $\newline$ The missing number should be $5$ .
Verify Pattern: Verify the pattern by checking if the sequence is correct with the missing number filled in. $\newline$ $1, 5, 7, 13, 21, 31, 43, 57$ $\newline$ Check the differences again: $\newline$ $5 - 1 = 4$ $\newline$ $7 - 5 = 2$ $\newline$ $13 - 7 = 6$ $\newline$ $21 - 13 = 8$ $\newline$ $31 - 21 = 10$ $\newline$ $43 - 31 = 12$ $\newline$ $57 - 43 = 14$ $\newline$ The pattern of differences $(4, 2, 6, 8, 10, 12, 14)$ does not increase by $2$ each time, which means there is a mistake.