Final answer:
To find the n-th term of the sequence, calculate the common difference, determine the first term, and then apply the formula for the n-th term of an arithmetic sequence.
Step-by-step explanation:
To find the nth term of an arithmetic sequence, we need to determine the common difference. The common difference is the difference between any two consecutive terms in the sequence. In this case, we can find the common difference by subtracting the third term from the fifth term.
-3.28 - (-3.14) = -3.28 + 3.14 = -0.14
Now, we can use the common difference (-0.14) and the third term (-3.14) to find the first term of the sequence. Subtracting 2 common differences from the third term gives us:
-3.14 - 2(-0.14) = -3.14 + 0.28 = -2.86
Therefore, the first term of the sequence is -2.86. Now, we can use the formula for the nth term of an arithmetic sequence:
Tn = a + (n-1)d
where Tn is the nth term, a is the first term, n is the position of the term, and d is the common difference.
Plugging in the values, we have:
Tn = -2.86 + (n-1)(-0.14)
Simplifying the expression:
Tn = -2.86 - 0.14n + 0.14
Tn = -2.72 - 0.14n
Therefore, the nth term of the sequence is -2.72 - 0.14n.