We can write the arithmetic sequence as $a, a+d, a+2d, a+3d, \dots$,
where $a$ is the first term and $d$ is the common difference.
We are given that the 3rd term is 17, so we have $a+2d=17$.
We are also given that the 5th term is 39, so we have $a+4d=39$.
Subtracting the first equation from the second equation, we get $2d=22$, or $d=11$.
Substituting this value back into the first equation, we get $a+2(11)=17$, or $a=-5$.
Now we can find the 7th term by adding 6 times the common difference to the first term: $-5+6(11)=\boxed{61}$.
The answer is: 61
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
In an arithmetic sequence, the 3rd term is 17 and the 5th term is 39. What is the value of the 7th term in the same sequence?

### Answer:
