# SOLUTION: How do you find the no. of terms in the following geometic sequence. 36+12+4+----+4/27. I know the formular but I seem to be getting the answer wrong.

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 Click here to see ALL problems on Geometric formulas Question 208991: How do you find the no. of terms in the following geometic sequence. 36+12+4+----+4/27. I know the formular but I seem to be getting the answer wrong.Answer by Edwin McCravy(8924)   (Show Source): You can put this solution on YOUR website!How do you find the no. of terms in the following geometic sequence. 36, 12, 4, ..., . I know the formula but I seem to be getting the answer wrong. ``` To find the common ratio, r, we divide any term by its preceding term. So we can either divide the second term 12 by the first term 36 and get which reduces to . So or we can divide the third term 4 by the second term 12 and get which also reduces to . So either way we get . I'll do it two ways, the first way we'll do it will not be acceptable to your teacher, but it gets the right answer, so you'll know when you get it right. The first way is to write the terms out till you get to by multiplying by each time: 36, 12, 4, So to get the next term we multiply 4 by and get . So far we have: 36, 12, 4, , To get the next term we multiply 4/3 by and get . So far we have: 36, 12, 4, , To get the next term we multiply 4/9 by and get . So that's it, we now have 36, 12, 4, , , Then we count the terms and see that there are 6. But your teacher doesn't want you to do that in case there might have been 100 terms! But at least we know the answer is 6. Here's what your teacher wants to to do: The formula for the nth term of a geometric sequence is Cross multiply: Simplify by dividing both sides by 4: Write and and as Add exponents on the right: Use the principle: If and and then Edwin```