9514 1404 393
Answer:
-1
Step-by-step explanation:
We notice that we want term a1 and have terms a17 and a33. These terms (every 16-th term) form an arithmetic sequence. The middle term (a17) is the average of the other two, so we have ...
a17 = (a1 +a33)/2
2a17 -a33 = a1 = 2(10) -21 = -1
a1 = -1
_____
Additional comment
You could go to the trouble to find the general term of the sequence.
an = a1 +d(n -1)
a17 = a1 + d(17 -1) = 10
a33 = a1 + d(33 -1) = 21
Subtracting the first equation from the second, we have ...
16d1 = 11
d1 = 11/16
Using the first equation, we find ...
a1 +(11/16)(17 -1) = 10
a1 = 10 -11 = -1 . . . . same as above.
