Use of Sigma Notation (Arithmetic)
Key points
- Arithmetic Series can be written in summation, or sigma notation.
- The elements of sigma notation are the upper and lower limits, and a formula for the terms.
Sigma Notation is the shorthand way to write the sum of a finite arithmetic series.
- It is based on the Greek letter sigma.
- The lower limit, at the bottom of the expression, is the number of term you are starting at.
- The upper limit, at the top of the expression, is the number of the last term of the finite arithmetic series.
- The expression on the right hand side of sigma notation is the formula for the value of a term based on the term number.
Expressing a finite arithmetic series in sigma notation requires derivation of the different elements, as seen to the left
- Find the common difference.
- Substitute this common difference and the value of the first term back into the equation to derive an expression for the value of the term based on the number of the term.
- Use this derived expression to find the upper limit.
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