Final answer:
To determine the nth term of an arithmetic sequence, we can use the formula 'a_n = a_1 + (n-1)d', where a_n is the nth term, a_1 is the first term, and d is the common difference. In this case, given the third term is 19 and the fifth term is 39, we can solve a system of equations to find the values of a_1 and d. Substituting the values back into the formula, we find that the nth term is -1 + (n-1)10.
Step-by-step explanation:
To determine the nth term of an arithmetic sequence, we can use the formula:
an = a1 + (n-1)d
where an is the nth term, a1 is the first term, and d is the common difference.
In this case, we are given that the third term is 19 and the fifth term is 39. We can start by plugging these values into the formula:
19 = a1 + 2d
39 = a1 + 4d
Now, we can solve this system of equations to find the values of a1 and d.
Subtracting the first equation from the second equation, we get:
20 = 2d
Dividing both sides by 2, we find that d = 10.
Substituting the value of d back into the first equation, we have:
19 = a1 + 20
Subtracting 20 from both sides, we find that a1 = -1.
So, the formula for the nth term of this arithmetic sequence is:
an = -1 + (n-1)10