Every month the price of a particular commodity falls in this order:
1024, 640, 400, 250, $\ldots$
What is the next value?
Please help me to find pattern of this sequence.
Each subsequent number is $\frac58$ of the previous one.
According to the On-line encyclopedia of integer sequences
A084912:$~~$ a(1) = 1024;$~~$ a(n) = 5*a(n-1)/8.
Puzzle: a man offered to sell me a car two years ago for \$1024; a year later his price was \$640; a little while after that he asked \$400; and last week he was willing to sell for \$250. The next time he reduces I shall buy. At what price will I buy the car if he makes consistent reductions?
Answer: a(5) = 1250/8 = \$156.25 (not an integer).