confused+ math!

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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.

  • confused+ math! -

    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

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