Geometric Series: Find 3 Numbers for 5 Components

In summary, the conversation discusses how to enter 3 numbers between 31 and 496 to create an increasing geometric series with 5 components. The suggestion is made to multiply instead of add to get the successive terms in the series. The poster expresses gratitude for the help.
  • #1
Femme_physics
Gold Member
2,550
1

Homework Statement



You must enter 3 numbers between 31 and 496 so there will be an increasing geometric series with 5 components.


The Attempt at a Solution



It tells me I'm off. That q=2. But how?

http://img716.imageshack.us/img716/8895/300xk.jpg
 
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  • #2
Hey FP :)

Multiply instead of add?
 
  • #3
With a geometric series, you multiply by q to get successive terms:

[tex]\begin{align*}
a_2 & = a_1 q \\
a_3 & = a_1 q^2 \\
a_4 & = a_1 q^3 \\
a_5 & = a_1 q^4
\end{align*}[/tex]

Do you see your mistake now?
 
  • #4
I like Serena said:
Hey FP :)

Multiply instead of add?


w00t! :) I hope I have all the formulas at the test so I can relook them. Thanks, ILS! And vela, too :)
 

FAQ: Geometric Series: Find 3 Numbers for 5 Components

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 factor. It follows the formula a, ar, ar^2, ar^3... where a is the first term and r is the common ratio.

2. How do you find 3 numbers for 5 components in a geometric series?

To find 3 numbers for 5 components in a geometric series, you need to know the first term, common ratio, and number of terms. Then, you can use the formula ar^2, ar^3, and ar^4 to find the second, third, and fourth terms respectively.

3. What is the formula for finding the sum of a geometric series?

The formula for finding the sum of a geometric series is S = a(1-r^n)/(1-r), where S is the sum, a is the first term, r is the common ratio, and n is the number of terms.

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

Yes, a geometric series can have a negative common ratio. This means that the terms in the series will alternate between positive and negative values.

5. What is the difference between an infinite and finite geometric series?

An infinite geometric series has an infinite number of terms, while a finite geometric series has a specific number of terms. Additionally, an infinite geometric series may or may not have a finite sum, while a finite geometric series will always have a finite sum.

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