Math Problem Statement
Determine the summation notation for the series 3 + 9 + 27+81+243
Solution
The given series is:
This is a geometric series where the first term and the common ratio , because each term is multiplied by 3 to get the next term.
General Formula for a Geometric Series
A geometric series can be written as:
Where:
- is the first term,
- is the common ratio,
- is the number of terms.
For the given series:
- ,
- ,
- Number of terms .
Thus, the summation notation for the given series is:
Or equivalently:
This represents the sum of the terms .
Would you like any further details or clarifications?
Here are five related questions you could explore:
- What is the sum of this geometric series?
- How does the formula change for an infinite geometric series?
- What happens if the common ratio is less than 1?
- Can you generalize this series for any number of terms?
- How do you find the sum of a finite geometric series?
Tip: In geometric series, the sum can be found easily using the formula if .
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometric Series
Formulas
General formula for geometric series: S_n = a + ar + ar^2 + ... + ar^(n-1)
Summation notation: ∑_{k=0}^{n-1} a * r^k
Theorems
Geometric series summation formula
Suitable Grade Level
Grades 9-12