Final answer:
To find the nth term of an arithmetic sequence with terms -1.02 and -1.04 for the third and fifth positions respectively, we calculate the common difference, find the first term, and then use the general formula for the nth term. The nth term is -1.01 - 0.01(n-1).
Step-by-step explanation:
To determine the nth term of an arithmetic sequence when given that the third term is -1.02 and the fifth term is -1.04, we first need to find the common difference of the sequence. Using the formula for the nth term of an arithmetic sequence, which is an = a1 + (n-1)d, we can find the common difference (d) using the given terms.
Let's denote the first term by a1 and the common difference by d. Since the third term is -1.02, we can write it as: a3 = a1 + 2d = -1.02. Similarly, for the fifth term, which is -1.04, we have: a5 = a1 + 4d = -1.04. Subtracting the first equation from the second provides: 2d = -0.02, hence d = -0.01.
Now we have the common difference, we can find the first term by substituting d back into the equation for a3: a1 = -1.02 - 2(-0.01) = -1.02 + 0.02 = -1.00.
Finally, the formula for the nth term of this arithmetic sequence is an = -1.00 + (n-1)(-0.01), which simplifies to an = -1.01 - 0.01(n-1).