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Arithmetic Progression — Part 2: Sum of the first n terms and applications

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Lesson

Arithmetic Progression, Part 2

Add the terms of an AP one after another and the running totals grow faster and faster. One formula gives any total at once.

In this lesson you will

  • Find the sum of the first n terms of an AP with either form of the sum formula
  • Find the number of terms when the sum is given
  • Find terms from a rule for the sum, and the sum of a block of terms
  • Solve real-life problems such as savings and instalments that change by a fixed amount
  • Sn=1.5n2+2.5nS_n = 1.5n^2 + 2.5n
The terms rise steadily, so the totals grow faster and faster.