Type the missing number in this sequence: 1, 3, 7, _____, 21, 31, 43

Identify Pattern: Identify the pattern in the sequence. Look at the differences between the numbers to see if there is a consistent pattern. 1 to 3 is an increase of 2. 3 to 7 is an increase of 4. If the pattern is increasing by consecutive even numbers, the next difference should be 6.Apply Pattern: Apply the pattern to find the missing number. Add 6 to the third term (7) to find the fourth term. 7 + 6 = 13Verify Continuation: Verify the pattern continues after the missing number. Add the next consecutive even number, which is 8, to the number we found for the missing term (13). 13 + 8 = 21 This matches the next number in the sequence, so the pattern is correct.Check Remaining Numbers: Check the pattern with the remaining numbers. Add the next consecutive even number, which is 10, to 21 to see if it matches the next number in the sequence. 21 + 10 = 31 This matches the next number in the sequence. Then, add the next consecutive even number, which is 12, to 31. 31 + 12 = 43 This matches the last number in the sequence, confirming the pattern.

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Type the missing number in this sequence: $\newline$ $1$ , $3$ , $7$ , _____, $21$ , $31$ , $43$

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Algebra 1

Sequences: mixed review

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Q. Type the missing number in this sequence:

\newline

1

3

7

, _____,

21

31

43

Identify Pattern: Identify the pattern in the sequence. $\newline$ Look at the differences between the numbers to see if there is a consistent pattern. $\newline$ $1$ to $3$ is an increase of $2$ . $\newline$ $3$ to $7$ is an increase of $4$ . $\newline$ If the pattern is increasing by consecutive even numbers, the next difference should be $6$ .
Apply Pattern: Apply the pattern to find the missing number. Add $6$ to the third term ( $7$ ) to find the fourth term. $7 + 6 = 13$
Verify Continuation: Verify the pattern continues after the missing number. Add the next consecutive even number, which is $8$ , to the number we found for the missing term ( $13$ ). $13 + 8 = 21$ This matches the next number in the sequence, so the pattern is correct.
Check Remaining Numbers: Check the pattern with the remaining numbers. $\newline$ Add the next consecutive even number, which is $10$ , to $21$ to see if it matches the next number in the sequence. $\newline$ $21 + 10 = 31$ $\newline$ This matches the next number in the sequence. $\newline$ Then, add the next consecutive even number, which is $12$ , to $31$ . $\newline$ $31 + 12 = 43$ $\newline$ This matches the last number in the sequence, confirming the pattern.