How to Find the Ratio in a Geometric Progression with Non-Consecutive Terms

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In summary, the person is having trouble with finding the ratio in a geometric progression given the 7th and 26th terms. They usually can solve it by finding the first term, but are unsure how to do it when the terms are far apart. Another person suggests using the constant ratio property of geometric progressions to solve for the missing term. The person is grateful for the help and feels prepared for their math test tomorrow.
  • #1
Olly
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I am having toruble with my geometric progressions, in that i ahv ebeen given a question where i am given the 7th and 26th terms of a GP. I am required to find the ratio however, which i could do if i had the first term. Usually i can do this as they only give me gps that are one term apart, and i would divide the top by bottom (say Term6 = 3 and term7 = 4) and woudl end up with term1 = 3/4. How can i do this if the terms are as far apart as they are?

Welcoming any responses here :smile:
 
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  • #2
Olly said:
I am having toruble with my geometric progressions, in that i ahv ebeen given a question where i am given the 7th and 26th terms of a GP. I am required to find the ratio however, which i could do if i had the first term. Usually i can do this as they only give me gps that are one term apart, and i would divide the top by bottom (say Term6 = 3 and term7 = 4) and woudl end up with term1 = 3/4. How can i do this if the terms are as far apart as they are?

Welcoming any responses here :smile:
i think you have too many variables such as a1 and n (the number of terms) that are unknown at least one of them are needed to solve for the quotinent.
 
  • #3
You know that in a geometric progression, the next term's ratio with the previous is a constant; let's call it x; that is GP(n+1)/GP(n)=x.
But then we must have: GP(n+2)/GP(n)=(GP(n+2)/GP(n+1))*GP(n+1)/GP(n)=x^(2).
Did that help?
 
  • #4
Thanks for the help, I've got it down pat now :) hope I am ready for maths test tomorrow :wink:
 

1. What is a geometric progression?

A geometric progression is a sequence of numbers in which each term after the first is found by multiplying the previous term by a constant number called the common ratio. For example, in the sequence 1, 2, 4, 8, 16, the common ratio is 2.

2. How do you find the common ratio of a geometric progression?

The common ratio of a geometric progression can be found by dividing any term in the sequence by the previous term. This will give you the same value for all ratios in the sequence.

3. What is the formula for finding the nth term in a geometric progression?

The formula for finding the nth term in a geometric progression is an = a1 * rn-1, where an is the nth term, a1 is the first term, and r is the common ratio.

4. Can a geometric progression have a negative common ratio?

Yes, a geometric progression can have a negative common ratio. This will result in a sequence that alternates between positive and negative values.

5. How is a geometric progression used in real-life applications?

Geometric progressions can be used to model situations where the rate of change remains constant. This can be seen in financial investments, population growth, and radioactive decay. They can also be used to create visual art, such as fractals, and in music theory to create harmonies and melodies.

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