Final answer:
To find the nth term of an arithmetic sequence, we need to determine the common difference and use the formula nth term = first term + (n-1) * common difference.
Step-by-step explanation:
To find the nth term of an arithmetic sequence, we need to identify the common difference between each term. From the given information, we can see that the third term is -1595 and the fifth term is -3195. Using these values, we can determine the common difference by subtracting the third term from the fifth term: -3195 - (-1595) = -3195 + 1595 = -1600.
To find the nth term, we can use the formula: nth term = first term + (n-1) * common difference. Given that the third term is -1595, we can substitute the values into the formula: -1595 = first term + (3-1) * -1600. Solving for the first term, we get: first term = -1595 - 2*(-1600) = -4795.
Finally, we can substitute the first term and the common difference into the formula to find the nth term: nth term = -4795 + (n-1) * -1600. This gives us the formula for the nth term of the sequence.
Now the nᵗʰ term of an arithmetic sequence is given by the formula an = a1 + (n - 1)d, where an is the nᵗʰ term, a1 is the first term, n is the term number, and d is the common difference. To find the first term (a1), we use the third term as a reference: -1595 = a1 + 2(-800), which gives a1 = -1595 - 2(-800) = -1595 + 1600 = 5.
So the formula for the nᵗʰ term becomes an = 5 + (n - 1)(-800). This is a direct calculation for any nᵗʰ term in the sequence.