How Do You Solve a Geometric Progression with Sum and Term Constraints?

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In summary, for an infinite geometric progression to have a finite sum, the first term and common ratio must be found. In this case, the sum of the first two terms is 9 and the third term is 12. Using the equations a + ar = 9 and ar2 = 12, the values of the first term and common ratio can be solved.
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jinx007
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An infinite geometric progression has a finite sum. Given that the sum of the first two terms is 9 and the third term is 12.

1/ Find the value of the first term and the common ration r.
 
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Work shown?
 
  • #3
thrill3rnit3 said:
Work shown?

what? i cannot really understand what you r saying
i just need help..lolzz...in fact don't really know where to start..y the way i know the equation
 
  • #4
jinx007 said:
what? i cannot really understand what you r saying
i just need help..lolzz...in fact don't really know where to start..y the way i know the equation

Well, I can't just spoonfeed you with the answer.

A geometric progression can be written as a, ar, ar2, ar3,..., arn

Where a is the first term, and r is the common ratio

If the sum of the first two terms is 9, we can rewrite that as

a + ar = 9

If the third term is 12, we can rewrite it as

ar2 = 12

Now you have 2 equations in 2 unknowns. I think it should be solvable now.
 

1. What is a geometric progression?

A geometric progression is a sequence of numbers where each term is obtained by multiplying the previous term by a constant value called the common ratio. For example, in the sequence 2, 6, 18, 54, the common ratio is 3.

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

The common ratio in a geometric progression can be found by dividing any term by the previous term. This will give you the same value for all terms 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 * r^(n-1), where an is the nth term, a1 is the first term, and r is the common ratio.

4. What is the sum of a finite geometric progression?

The sum of a finite geometric progression can be found using the formula Sn = a1 * (1-r^n)/(1-r), where Sn is the sum of the first n terms, a1 is the first term, and r is the common ratio.

5. How is geometric progression used in real life?

Geometric progression is used in various fields such as finance, engineering, and science. It can be used to model population growth, interest rates, and the decay of radioactive substances. It is also used in creating computer algorithms and in analyzing data in statistics.

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