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Questions tagged [geometric-progressions]

A geometric progression is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence

A geometric progression is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence. This can be useful when evaluating (in)finite series or determining a closed form for a recurrence relation.

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How to find number of terms in a geometric progression

What is the equation two find the number of terms in the geometric progression given first two and the last term?
Anon
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Given that 2m-8, 2m+4 and 5m-2 are successive terms of a geometric sequence. Find the value of m and thus the summation of the first 10 elements.

I don't want the answer to this question, rather just whether it is actually possible. So far I have found m = 10 and r = 2 (or alternatively m = 0 and r = -1/2) which gives the consecutive terms listed in the question values of 12, 24 and 48 (or…
Alfonsobonso
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Summation of a Summated variable

Question: Find $\sum_{k=1}^n u_k $ if $ u_n= \sum_{k=0}^{n} \frac{1}{2^k}$ My try : $u_1=\frac{1}{2^0}+\frac{1}{2^1} , u_2=\frac{1}{2^0}+\frac{1}{2^1}+\frac{1}{2^2} , u_n=\frac{1}{2^0}+\frac{1}{2^1}+\frac{1}{2^2} +...\frac{1}{2^n}…
Kartik Watwani
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Find the sum of the first $3n$ terms of a geometric series given the sum of the first $n$ terms is $48$ and the sum of first $2n$ terms is $60$

In a certain geometric series, the sum of the first $n$ terms is $48$ and the sum of the first $2n$ terms is $60$. Find the sum of the first $3n$ terms. $$48= a_1\frac{1-r^n}{1-r}$$ What do I do after this?
Kimmie
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a=b+b^2+b^3+b^4...Value of b lies between -1/2 and 1/2. GP a-a^2+a^3-a^4... is to be found.

Based upon this info, we are to find $a$-$a^2$+$a^3$-$a^4$... I could find that $a$=$b$/$(1-b)$ as it is infinite geometric progression. I tried doing mathematical induction but was stuck with a very tedious answer. Is there any better method for…
Minhaz Pathan
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