Final answer:
The first term of the arithmetic sequence is -1/2.
Step-by-step explanation:
The first term of an arithmetic sequence can be found using the formula: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.
In this case, we are given a27 = -1/2, so n = 27. We need to find a1 and the common difference. Let's plug in the values we know:
a27 = a1 + (27 - 1)d = -1/2
Simplifying this equation, we get:
a1 + 26d = -1/2
Now, we need one more equation to solve for a1 and d. We can use the fact that a1 + d = a2. Given that a27 = -1/2, we can calculate a2:
a1 + d = -1/2
Subtracting the equations, we get:
25d = 0
Therefore, the common difference, d, is 0. Now we can substitute this value back into either equation to find a1:
a1 + 26(0) = -1/2
a1 = -1/2
So, the first term of the arithmetic sequence is -1/2.