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​12345678910ε = 0.2

A ball is dropped and its first rebound reaches 8 m. Every next rebound reaches 60% of the previous one. Which rebound n is the first one lower than 0.2 m?

a₁ = 8r = 0.6ε = 0.2
n =
2.Easy
kak​13579111315ε = 0.1

The geometric sequence aₙ = 8·0.7ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.1.

a₁ = 8r = 0.7ε = 0.1
n =
3.Medium
xx₀ = 0??R

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

Σ 25ᵏx²ᵏ/kx₀ = 0
R =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ k·5ᵏ·xᵏ.

Σ k·5ᵏ·xᵏx₀ = 0
R =
5.Hard

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1·0.75ᵏ/k.

ak = (−1)k+1·0.75ᵏ/k
S =
6.Hard

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

ak = (−1)k+1/k
S =

Answer key

  1. 1. n = 9
  2. 2. n = 14
  3. 3. R = 0.2
  4. 4. R = 0.2
  5. 5. S = 0.5596
  6. 6. S = 0.6931

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