14. In a sequence, each term after the first two terms is the mean of all the terms which come before that term. The first term is 8 and the tenth term is 26 . What is the second term?
A 17
B 18
C 44
D 52
E 68
14. C Suppose the first three terms of the sequence are $a, b, c$. Then $c=\frac{1}{2}(a+b)$ and so $a+b=2 c$. The mean of the first three terms is then $\frac{1}{3}(a+b+c)=\frac{1}{3}(2 c+c)=c$, so the fourth term is $c$. Similarly, the following terms are all equal to $c$. Since one of these terms is 26 and $a=8$ then $b=2 c-a=52-8=44$.