Final answer:
The equation for the nth term of the arithmetic sequence is a_n = 1/2 * n. To find the ninth term in the sequence, substitute n with 9, yielding a_9 = 4.5.
Step-by-step explanation:
To find the equation for the nth term of an arithmetic sequence, one needs to identify the first term (a1) and the common difference (d) between the terms. The given sequence is 1/2, 1, 1 1/2, 2..., so the first term a1 is 1/2 and the common difference d is 1/2 (since each term increases by 1/2).
The general formula for the nth term of an arithmetic sequence is:
an = a1 + (n - 1)d
Plugging the values of a1 and d into the formula, we get:
an = 1/2 + (n - 1)(1/2)
Which simplifies to:
an = 1/2 * n
To find the ninth term (a9), we substitute n with 9:
a9 = 1/2 * 9 = 4.5