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Optional Mathematics · Class 10 · Sequence and Series
Sum of the First n Terms of an Arithmetic Series
Two formulas for Sₙ · Natural, even and odd numbers · Finding a, d, n or a term
By the end of this lesson you can
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Explain why Sₙ = n/2 (a + l)
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Use Sₙ = n/2 [2a + (n − 1)d]
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Add natural, even and odd numbers quickly
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Find n, d, a or a term from a given sum
The pairing trick
1 + 2 + 3 + ... + 10 in four moves
WRITE
Write the series forwards: 1 + 2 + ... + 10
REVERSE
Write it backwards underneath: 10 + 9 + ... + 1
ADD
Every column makes 11, and there are 10 columns: 110
HALVE
That is twice the sum, so the sum is 55
Presenter notes: Today we learn how to add a long arithmetic series in a few lines instead of adding term after term.