Sequences & series worksheet with answers

Free printable Sequences & series worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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Name: ____________________   Date: ____________

1.Easy
kak​13579111315ε = 0.5

The geometric sequence aₙ = 5·0.9ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.5.

a₁ = 5r = 0.9ε = 0.5
n =
2.Easy
kak​135791113ε = 0.2

The geometric sequence aₙ = 5·0.75ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.2.

a₁ = 5r = 0.75ε = 0.2
n =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 3/(k(k + 4)).

ak = 3/(k(k + 4))
S =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 2/(k(k + 1)).

ak = 2/(k(k + 1))
S =
5.Hard

Recognise the series and find its sum: S = Σk=1∞ k·0.2ᵏ.

ak = k·0.2ᵏ
S =
6.Hard

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1·0.5ᵏ/k.

ak = (−1)k+1·0.5ᵏ/k
S =

Answer key

  1. 1. n = 23
  2. 2. n = 13
  3. 3. S = 1.562
  4. 4. S = 2
  5. 5. S = 0.3125
  6. 6. S = 0.4055

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