Number of Terms in Geometric Progression 0.03 to ar^n-1

Thread starter jack15379
Start date May 29, 2010
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Geometric

In summary, the number of terms in a geometric progression can be found using the formula n = logr(an/a1), where n is the number of terms, r is the common ratio, an is the last term, and a1 is the first term. This formula can also be used to find the number of terms if the common ratio is not given, and can result in decimal values. If the common ratio is 2, you can take the logarithm of the last term divided by the first term and add 1 to find the number of terms.

May 29, 2010

jack15379

find the number of terms in 0.03+0.06+0.12+...+ar^n-1

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May 29, 2010

tiny-tim

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Related to Number of Terms in Geometric Progression 0.03 to ar^n-1

1. How do I find the number of terms in a geometric progression?

The number of terms in a geometric progression can be found by using the formula n = log_r(a_n/a₁), where n is the number of terms, r is the common ratio, a_n is the last term, and a₁ is the first term.

2. What is the formula for finding the number of terms in a geometric progression?

The formula for finding the number of terms in a geometric progression is n = log_r(a_n/a₁), where n is the number of terms, r is the common ratio, a_n is the last term, and a₁ is the first term.

3. Can the number of terms in a geometric progression be a decimal?

Yes, the number of terms in a geometric progression can be a decimal. This is because the formula for finding the number of terms uses logarithms, which can result in decimal values.

4. How can I determine the number of terms in a geometric progression if the common ratio is not given?

If the common ratio is not given, you can use the formula n = log_r(a_n/a₁) and solve for r. Once you have the value of r, you can use it in the formula to find the number of terms.

5. Is there a shortcut for finding the number of terms in a geometric progression if the common ratio is 2?

Yes, if the common ratio is 2, you can simply take the logarithm of the last term divided by the first term and add 1. This will give you the number of terms in the geometric progression.