Math Problem Statement
Solution
The sum provided in the image is:
We need to express this sum using sigma notation. To break this down:
- The first term is 5, and the last term is -7.
- The terms decrease by 1 for each successive term, starting at 5 and ending at -7.
Thus, we can express this as:
Here’s the breakdown:
- gives ,
- gives ,
- and so on, until , which gives .
This sum is written in sigma notation as:
Let me know if you need further clarifications or help with another concept!
Related questions for you:
- What is the sum of this series if you compute it manually?
- How would you express this sum if the terms were increasing by 2 instead of decreasing by 1?
- What is the formula for the sum of an arithmetic series?
- Can you write the sum of all even numbers between 1 and 20 using sigma notation?
- What changes to the formula would be needed if we started at a different number than 6?
Tip: When writing a sum in sigma notation, identify the pattern in the terms and express it as a function of the summation index.
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Math Problem Analysis
Mathematical Concepts
Sigma Notation
Arithmetic Sequences
Formulas
Σ notation for summation
Arithmetic sequence formula
Theorems
Sum of an arithmetic series
Suitable Grade Level
Grades 7-9
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