What Is the Value of 'a' in the Infinite Geometric Series?

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Homework Help Overview

The discussion revolves around finding the value of 'a' in an infinite geometric series represented by the expression 3 + 3a + 3a² + ... which is said to equal 45/8, with the condition that a > 0.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the appropriate formula for the sum of an infinite geometric series, with some confusion regarding the use of terms related to finite series. Questions arise about the implications of having an infinite number of terms and the behavior of the ratio as it approaches infinity.

Discussion Status

There is an ongoing exploration of the correct formula to apply for the infinite series, with some participants suggesting the need to clarify the conditions under which the series converges. Guidance has been offered regarding the correct approach to the problem, but no consensus has been reached on the specific value of 'a'.

Contextual Notes

Participants note the importance of the condition -1 < r < 1 for convergence in the context of infinite series, which is relevant to the discussion of the ratio 'r' in the series.

lionel messi.
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Sequences and series help...

1. Homework Statement
3+3a+3a^2+...∞ is = to 45/8 where a>0,then a is...?


3. The Attempt at a Solution
since it is a g.p so using
S=(a(rn-1))/(r-1) for r>1
ive all the values except for "n"..can someone help...:/
 
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lionel messi. said:
S=(a(rn-1))/(r-1) for r>1
ive all the values except for "n"..can someone help...:/
Wrong formula. This is an infinite geometric series, so use
a + ar + ar^2 + ar^3 + ... = \frac{a}{1 - r}
 


thanks..
 


n is the number of terms, so in this case there are infinite terms.
As n tends to infinity, what does r^n tend to? (Assuming -1<r<1)
This gets you to the formula that eumyang posted.
 

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