Final answer:
Using inductive reasoning and the formula for an arithmetic sequence, we determined that the 10th term of the sequence 3, 7, 11, 15, etc. is 39. This is found by adding 9 times the common difference (4) to the first term (3), which results in 39.
Step-by-step explanation:
The student is looking to use inductive reasoning to find the 10th number in the sequence 3, 7, 11, 15, etc. To solve this problem, first, we need to determine the pattern of the sequence. Looking at the sequence, we see that each number increases by 4 from the previous one (7 - 3 = 4, 11 - 7 = 4, and so on). This means we are dealing with an arithmetic sequence where the common difference (d) is 4.
To find the nth term in an arithmetic sequence, we use the formula:
Tn = a + (n - 1) • d,
where Tn is the nth term, a is the first term in the sequence, and n is the term number we want to find.
Applying this to our sequence with a = 3, d = 4, and n = 10, we get:
T10 = 3 + (10 - 1) • 4
T10 = 3 + 9 • 4
T10 = 3 + 36
T10 = 39.
Therefore, the 10th number in the sequence is 39, which is not listed in the provided options, so there might be an error in the options or in the question.