This will give you the value of , and then you can work out the terms in between.
Let the number be . Then the terms and are in geometric sequence. In other words:Find a number which when added to each of -1,1 and 5 gives 3 terms in geometric sequenceSolve this equation for .
With the usual notation, the sum of the first terms is:The sum of the first 8 terms of a geometric series is 17 times the sum of its first 4 terms. Find the common ratio.So:This is easy to solve if you spot that , and so the equation simplifies considerably!