Final answer:
The value of a(15) in the arithmetic sequence with a first term of 4 and a second term of 16 is found by using the formula a(n) = a(1) + (n - 1) * d, which yields a(15) = 172.
Step-by-step explanation:
To find the value of a(15) in an arithmetic sequence where a(1) = 4 and a(2) = 16, we first need to determine the common difference d. The common difference is found by subtracting the first term from the second term: d = a(2) - a(1) = 16 - 4 = 12.
Once we have the common difference, we can use the formula for the n-th term of an arithmetic sequence: a(n) = a(1) + (n - 1) * d. Substituting the known values, the formula to find a(15) becomes a(15) = 4 + (15 - 1) * 12.
Performing the arithmetic, we get a(15) = 4 + 14 * 12, which simplifies to a(15) = 4 + 168 = 172. Therefore, the value of a(15) in this arithmetic sequence is 172.