courses › Algebra

Find far-off terms and add up whole sequences.

Pen and paper is fine · no calculator needed why?

Learn first (about 3 minutes)

Opens at level 29.

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Builds on: Linear equations (not open yet) · Exponents & roots (not open yet)

skills · practice stats

From rounds of this course only: box, review and trial answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

• Arithmetic nth term par 18 s not tried yet

  worked example

  The sequence 4, 6, 8, … goes up by the same amount each time. What is the 46th term?

  Answer: 94

  1. The difference is 6 − 4 = 2.
  2. aₙ = a₁ + (n − 1)d = 4 + 45 × 2 = 94.

• Geometric nth term par 18 s not tried yet

  worked example

  The sequence 3, −6, 12, … is multiplied by −2 each time. What is the 5th term?

  Answer: 48

  1. aₙ = a₁ × r^(n − 1) = 3 × (−2)⁴ = 3 × 16 = 48.

• Arithmetic series par 25 s not tried yet

  worked example

  What is the sum of the first 16 terms of 6, 15, 24, …?

  Answer: 1,176

  1. Last term: 6 + 15 × 9 = 141.
  2. Sum = 16 × (6 + 141) ÷ 2 = 1,176.

• Infinite geometric sum par 25 s not tried yet

  worked example

  What is the sum of the infinite geometric series 38 + 57/2 + 171/8 + …? Give a fraction or a whole number.

  Answer: 152

  1. The ratio is (57/2) ÷ 38 = 3/4.
  2. The sum is a ÷ (1 − r) = 38 ÷ (1 − 3/4) = 38 ÷ (1/4) = 152.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

1. 1 day
2. 3 days
3. 7 days
4. 14 days
5. 30 days
6. 60 days
7. mastered · every 90 days

your rounds

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