Final answer:
The 10th term (a(10)) of an arithmetic sequence with a first term of 4 and a second term of 16 is found using the formula a(n) = a(1) + (n - 1)*d. The common difference is 12, and a(10) is 112.
Step-by-step explanation:
To find the value of a(10) in an arithmetic sequence where a(1) = 4 and a(2) = 16, we first need to determine the common difference of the sequence.
The common difference (d) is the difference between consecutive terms, so in this case, d = a(2) - a(1) = 16 - 4 = 12. An arithmetic sequence is defined by the formula a(n) = a(1) + (n - 1)*d. Therefore, to find a(10), we plug in our values into this formula to get a(10) = 4 + (10 - 1)*12 which is a(10) = 4 + 9*12.
Calculating further, a(10) = 4 + 108 = 112. Hence, the 10th term of the sequence, a(10), is 112.