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Flip to reveal answersWhat does the sigma symbol Σ mean?
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All 8 Flashcards — Sigma notation
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Question
What does the sigma symbol Σ mean?
Answer
Add up. Substitute the index from the lower limit to the upper limit into the expression and sum the results. Example: Σ r=1→4 of (2r+1) = 3+5+7+9 = 24.
Question
In sigma notation, what are the lower and upper limits?
Answer
The lower limit (below Σ) is where the index starts; the upper limit (above Σ) is where it stops. Both endpoints are included.
Question
How many terms are in a sigma sum?
Answer
Upper limit − lower limit + 1. Example: Σ r=2→9 has 9 − 2 + 1 = 8 terms.
Question
How do you know a sigma sum is an arithmetic series?
Answer
When the summand is linear in the index (like 3r + 2). The common difference equals the coefficient of the index.
Question
How do you evaluate Σ r=1→10 of (3r + 2) by hand?
Answer
First term 5, last term 32, n = 10; then S = (10/2)(5 + 32) = 185.
Question
For a sum of a linear term, how do you read u₁ and d?
Answer
u₁ = the summand at the lower limit; d = the coefficient of the index. Then use the arithmetic sum formula.
Question
What is the most common sigma mistake?
Answer
Counting terms as (upper − lower) and forgetting the +1, or assuming the index starts at 1.
Question
How can you evaluate a sigma sum on the GDC?
Answer
On Paper 2 use sum(seq(expression, index, lower, upper)). On Paper 1 you must use the arithmetic sum formula by hand.
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Topic 1.2 hub
Arithmetic sequences & series
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