Final answer:
To find the 12th term of the arithmetic sequence, use the recursive formula an = an-1 + 15 with a1 = 10. Substitute the values to find the 12th term.
Step-by-step explanation:
An arithmetic sequence is a sequence in which the difference between any two consecutive terms is constant. In this case, the sequence is defined by the formula an = an-1 + 15, where a1 = 10.
To find the 12th term of the sequence, we can use the formula:
a12 = a11 + 15
Substituting the value of a1 and using the recursive formula, we can find the 12th term as follows:
a2 = a1 + 15 = 10 + 15 = 25
a3 = a2 + 15 = 25 + 15 = 40
Continuing this pattern, we find that:
a12 = a11 + 15 = a10 + 15 + 15 = ... = a1 + (12-1) * 15 = 10 + 11 * 15 = 175
Therefore, the 12th term of the arithmetic sequence is 175.