confused+ math!
posted by Anonymous on .
A finite geometric sequence has t1= 0.1024 and t2= 0.256 how many terms does this sequence have if its middle temr has the value 156.25?
how would go about and do this question?
If t_{1} = 0.1024 and t_{2} = 0.256, then the common ratio is t_{2}/t_{1} = 2.5
The value at term n is given by .1024 * 2.5 ^{n1}, therefore solve
156.25 = .1024 * 2.5 ^{n1} to find the middle term.

guess and check on finding the middle term (it's 9) to get 18 terms
mathematically I thought you were supposed to log both sides
log156.25 = log(.1024*2.5)^n1
log156.25 = n1log(.256)<power of log rule
log156.25/log(.256) =n1
I did something wrong though... because my answer isn't right