Geometric series - positive and negative ratio

In summary, a geometric series is a sequence of numbers where each term is found by multiplying the previous term by a constant ratio. A positive ratio in a geometric series refers to a ratio that is greater than 0, while a negative ratio refers to a ratio that is less than 0. The sum of a geometric series can be found using the formula S = a / (1 - r), and the formula for finding the nth term is a * r^(n-1).
  • #1
jackcr
8
0
Hello,

Second term of a geometric series is 48 and the fourth term is 3... Show that one possible value for the common ratio, r, of the series is -1/4 and state the other value.

ar=48, ar^3= 3... so ar^3/ar=3/48 which simplifies to r^2 = 1/16, therefore r = 1/4

Can anyone explain where the other solution is from? Or where I am wrong

Thanks, and sorry if this is in the wrong section, I'm not familiar with pre/post calculus
 
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  • #2
Oh, nevermind its because I have rooted the 1/16 meaning it could have been + or - 1/4 to start with. Haha
 

1. What is a geometric series?

A geometric series is a sequence of numbers where each term is found by multiplying the previous term by a constant ratio. The first term is typically denoted as 'a' and the common ratio as 'r'.

2. What is a positive ratio in a geometric series?

A positive ratio in a geometric series refers to a ratio that is greater than 0. This means that each term in the series is increasing in value.

3. What is a negative ratio in a geometric series?

A negative ratio in a geometric series refers to a ratio that is less than 0. This means that each term in the series is decreasing in value.

4. How do you find the sum of a geometric series?

The sum of a geometric series can be found using the formula: S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio. This formula only works if the absolute value of the ratio is less than 1.

5. What is the formula for finding the nth term in a geometric series?

The formula for finding the nth term in a geometric series is: a * r^(n-1), where 'a' is the first term and 'r' is the common ratio. This formula can also be written as a * (r^n / r).

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