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Arithmetic series

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Useful for: MCR3U IB Math AA SL & HL IB Math AI SL & HL

Learn it The sum of the first n terms of an arithmetic series is Sₙ = n(a + tₙ)/2 = n[2a + (n − 1)d]/2: the number of terms times the average of the first and last.

Example: A stack of logs has 20 on the bottom row, 19 above, … up to 5 on top. Total logs?

  1. n = 16 rows, a = 20, last = 5.
  2. S = 16(20 + 5) ÷ 2 = 200 logs.

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