To find the next number in the given arithmetic sequence [tex]\(32, 37, 42\)[/tex], we need to follow a few steps.
1. Identify the Sequence and Define the Difference:
- The given sequence is [tex]\(32, 37, 42\)[/tex].
- To determine the pattern, we need to find the common difference between consecutive terms.
2. Calculate the Common Difference:
- The difference between the second and first term is [tex]\(37 - 32 = 5\)[/tex].
- Similarly, the difference between the third and second term is [tex]\(42 - 37 = 5\)[/tex].
- Hence, the common difference for this sequence is [tex]\(5\)[/tex].
3. Find the Next Term:
- The next number in an arithmetic sequence is found by adding the common difference to the last term in the sequence.
- The last term in the given sequence is [tex]\(42\)[/tex].
4. Compute the Next Number:
- Next number = Last term + Common difference = [tex]\(42 + 5 = 47\)[/tex].
Thus, the next number in the sequence [tex]\(32, 37, 42\)[/tex] is [tex]\(47\)[/tex], and the correct choice among the provided options is [tex]\(47\)[/tex].
So the answer is:
[tex]\[
\boxed{47}
\][/tex]
