Geometric series with modified terms

Thread starter kop442000
Start date Feb 22, 2013
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Geometric Geometric series Series Terms

In summary, a geometric series with modified terms is a sequence of numbers where each term is obtained by multiplying the previous term by a constant factor that may be altered in some way. This is different from a regular geometric series where the constant factor remains the same throughout. Common modifications to the constant factor include adding or subtracting a constant value or using a different mathematical operation. To determine the sum of a geometric series with modified terms, a modified formula can be used. These types of series can be applied in real-life situations such as population growth or finance to calculate the present or future value of investments or loans with varying interest rates.

Feb 22, 2013

kop442000

I am looking for a way to sum some numbers. I understand that if I want to sum pⁱ, I can use the geometric series:

[itex]\sum\limits_{i=0}^N p^{i} = \frac{1-p^{N+1}}{1-p}[/itex]

But can anyone help me with what to do when I need:

[itex]\sum\limits_{i=0}^N p^{i} q^{ti}[/itex]

where t is just a constant.

Thank you in advance of any help!

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Feb 22, 2013

JJacquelin

Let : [itex] P = p.q^{t}[/itex]

Related to Geometric series with modified terms

What is a geometric series with modified terms?

A geometric series with modified terms is a sequence of numbers in which each term is obtained by multiplying the previous term by a constant factor. However, in this type of series, the constant factor may be modified or altered in some way.

How is a geometric series with modified terms different from a regular geometric series?

In a regular geometric series, the constant factor remains the same throughout the series. However, in a geometric series with modified terms, the constant factor may vary or be altered in some way for each term.

What are some common modifications that can be made to the constant factor in a geometric series with modified terms?

Some common modifications include adding a constant value to the constant factor, subtracting a constant value from the constant factor, or using a different mathematical operation (such as division or exponentiation) on the constant factor.

How do you determine the sum of a geometric series with modified terms?

To determine the sum of a geometric series with modified terms, you can use the formula S = a/(1-r), where S is the sum, a is the first term in the series, and r is the common ratio (the constant factor in a regular geometric series). However, if the constant factor has been modified in some way, you will need to modify the formula accordingly.

What are some real-life applications of geometric series with modified terms?

Geometric series with modified terms can be used to model real-life situations, such as population growth or interest rates, where the growth or change is not constant but instead varies over time. They are also commonly used in finance and economics to calculate the present or future value of investments or loans with varying interest rates.