The numbers 4x,2x−3,4x−3 are three consecutive terms in an arithmetic sequence. What is the value of x?
A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.
Solution
Since 4x,2x−3,4x−3 form an arithmetic sequence, then the differences between consecutive terms are equal, or (2x−3)−4x=(4x−3)−(2x−3). Thus, −2x−3=2x or 4x=−3 and so x=−43.
Want a route through all this instead of an archive? The track
puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.
Source: Omni-MATH,
licensed Apache-2.0.
Statement reproduced verbatim; metadata (topic, difficulty) added by this project.