### Instruction: The 3rd and 5th terms of an arithmetic sequence are 17 and 39, respectively. What is the 7th term of the same sequence?### Response: To find the 7th term of an arithmetic sequence, I need to know the common difference between consecutive terms.
I can find the common difference by subtracting any two adjacent terms, such as the 3rd and 4th terms, or the 4th and 5th terms.
I don't know the 4th term, but I can use the fact that the 3rd and 5th terms are 17 and 39, respectively, to find it.
If I let d be the common difference, then the 4th term is 17 + d, and the 5th term is 17 + d + d, or 17 + 2d.
Since the 5th term is 39, I can set 17 + 2d equal to 39 and solve for d.
Subtracting 17 from both sides, I get 2d = 22.
Dividing both sides by 2, I get d = 11.
This means that the common difference is 11, and I can use it to find the 7th term.
The 7th term is the 5th term plus 2d, or 39 + 2(11), which is 61.