Question

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 t₁ = 0.1024 and t₂ = 0.256, then the common ratio is t₂/t₁ = 2.5
The value at term n is given by .1024 * 2.5 ^n-1, therefore solve
156.25 = .1024 * 2.5 ^n-1 to find the middle term.

Answer 1

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)^n-1
log156.25 = n-1log(.256)<--power of log rule
log156.25/log(.256) =n-1
I did something wrong though... because my answer isn't right