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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1.Easy
kak​13579111315ε = 0.1

The geometric sequence aₙ = 20·0.85ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.1.

a₁ = 20r = 0.85ε = 0.1
n =
2.Easy
kak​12345678910ε = 0.05

The geometric sequence aₙ = 10·0.5ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.05.

a₁ = 10r = 0.5ε = 0.05
n =
3.Medium
k|aₖ|¹ᐟᵏ123456789101112

Apply the root test to Σk=1∞ ((5k + 1)/(2k + 6))ᵏ. Find L = lim |ak|1/k.

ak = ((5k + 1)/(2k + 6))ᵏ
L =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 25ᵏx²ᵏ/k.

Σ 25ᵏx²ᵏ/kx₀ = 0
R =
5.Hard

Recognise the series and find its sum: S = Σk=1∞ k·0.25ᵏ.

ak = k·0.25ᵏ
S =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·22k/(2k)!.

ak = (−1)ᵏ·22k/(2k)!
S =

Answer key

  1. 1. n = 34
  2. 2. n = 9
  3. 3. L = 2.5
  4. 4. R = 0.2
  5. 5. S = 0.4444
  6. 6. S = −0.4161

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