Owen May
05/29/2023 · Middle School
Type the next number in this sequence: \( 1,3, \quad 7,13,21,31, \square \) Submit
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Step-by-step Solution
To find the next number in the sequence \( 1, 3, 7, 13, 21, 31, \square \), let's first look at the differences between consecutive terms:
- \( 3 - 1 = 2 \)
- \( 7 - 3 = 4 \)
- \( 13 - 7 = 6 \)
- \( 21 - 13 = 8 \)
- \( 31 - 21 = 10 \)
Now, we have the sequence of differences: \( 2, 4, 6, 8, 10 \).
The differences themselves form an arithmetic sequence where each term increases by \( 2 \). The next difference after \( 10 \) would be \( 12 \).
Now, we can find the next term in the original sequence by adding this difference to the last term:
\[
31 + 12 = 43
\]
Thus, the next number in the sequence is \( \boxed{43} \).
Quick Answer
The next number in the sequence is 43.
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