Question

The following sequence is an arithmetic sequence. You are not shown very many terms of this sequence, but you are shown enough to fill in the missing number. What number goes in the blank? 7,_,17...

Answer 1

12

since the difference of the first and third value is ten, each value is five more than the previous value

Answer 2

Remark
Since it is an arithmetic sequence and the first and third terms are given to you, the second term may be found by taking the average of the first and third terms.

t2 = (t1 + t2)/2
t2 = (7 + 17)/2
t2 = 24/2 
t2 = 12 Answer <<<<<

See if that works
7 12 17 The first two terms differ by 5. 
The second two terms differ by 5 So for this sequence, that works. 

Will you be able to do this with any any arithmetic sequence?
___, ___, 12 ___ 18

At least for this one, yes. The answer is 15. The first two terms are 6 and 9. 
How should you do it?

Discussion (This is extra. You don't have to read it)
You should do it by defining the terms using the term formula
tn = a + (n - 1)d
t5 = a + 2*d = 18
t3 = a + d = 12
d = 6
a = 6 as well.