Final answer:
To determine the nᵗʰ term of an arithmetic sequence, calculate the common difference from two given terms, and use it with the first term in the nᵗʰ term formula.
Step-by-step explanation:
To find the nth term of an arithmetic sequence when given two terms, we must first determine the common difference. In an arithmetic sequence, the difference between any two successive terms is constant. For the sequence where the third term is -3.2 and the fifth term is 1.6, we can find the common difference (d) using the following steps:
Find the difference between the fifth and third terms: 1.6 - (-3.2) = 1.6 + 3.2 = 4.8
Since there are two steps between the third and fifth terms, divide the difference by the number of steps to get the common difference: 4.8 / 2 = 2.4.
This is the amount each term increases by, so the common difference, d, is 2.4.
Now, we use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d. To find the first term (a1), we can work backwards from the third term:
Subtract two times the common difference from the third term to find the first term: -3.2 - (2 * 2.4) = -3.2 - 4.8 = -8.
So, the first term, a1, is -8.
With a1 and d determined, the nth term formula becomes an = -8 + (n - 1)(2.4).