Problem: The first four terms of an arithmetic sequence are a,x,b,2xa, x, b, 2 xa,x,b,2x. The ratio of aaa to bbb is
Answer Choices:
A. 1/41 / 41/4
B. 1/31 / 31/3
C. 1/21 / 21/2
D. 2/32 / 32/3
E. 222
Solution:
The difference between the second and fourth terms is xxx; thus the difference between successive terms is x/2x / 2x/2. Therefore a=x/2,b=3x/2a=x / 2, b=3 x / 2a=x/2,b=3x/2 and
ab=x/23x/2=13\dfrac{a}{b}=\dfrac{x / 2}{3 x / 2}=\dfrac{1}{3} ba​=3x/2x/2​=31​