Answer:
27
Step-by-step explanation:
The 2nd and 4th terms differ by 7-(-3) = 10. The difference between any terms that are 2 apart will be 10, so the 6th and 8th terms are ...
7 +10 = 17 . . . 6th term
17 +10 = 27 . . . 8th term
_____
A more conventional solution might have you find the equation for a general term. You would start with the form of that, then solve for the parameters of it.
an = a1 +d(n -1)
a2 = a1 +d(2 -1) = -3
a4 = a1 + d(4 -1) = 7
Subtracting the equation for a2 from that for a4, we get ...
a4 -a2 = (a1 +3d) -(a1 +d) = (7) -(-3)
2d = 10 . . . . . . simplify
d = 5 . . . . . . . . divide by 2 (common difference)
-3 = a1 +5 . . . . . substitute into equation for a2
-8 = a1 . . . . . . . .(first term of the sequence)
Now we know the general term can be found from ...
an = -8 +5(n -1)
Then the 8th term is ...
a8 = -8 +5(8 -1) = -8 +35 = 27 . . . . same as above
_____
<em>Alternate approach</em>
After you've done a few of these, you realize that the difference between terms 2 apart is twice the common difference. So, the common difference is ...
(7 -(-3))/2 = 5 . . . . as we found in the last section
You know the 4th term, so the general term can also be written as ...
an = a4 +d(n -4) . . . . . . note use of a4 and -4, instead of a1 and -1 above
an = 7 +5(n -4)
Now, the 8th term is computed as ...
a8 = 7 + 5(8-4) = 7 +20 = 27
