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​123456

Find the sum S6 of the first 6 terms of the geometric sequence 0.5, 0.25, 0.125, …

a₁ = 0.5r = 0.5n = 6
S6 =
2.Easy
kak​13579111315ε = 0.2

A ball is dropped and its first rebound reaches 8 m. Every next rebound reaches 75% of the previous one. Which rebound n is the first one lower than 0.2 m?

a₁ = 8r = 0.75ε = 0.2
n =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ kᵏ/(5ᵏ·k!). Find L = lim |ak+1/ak|.

ak = kᵏ/(5ᵏ·k!)
L =
4.Medium
k|aₖ|¹ᐟᵏ123456789101112

Apply the root test to Σk=1∞ ((3k + 2)/(2k + 5))ᵏ. Find L = lim |ak|1/k.

ak = ((3k + 2)/(2k + 5))ᵏ
L =
5.Hard

Find the coefficient c₂ of (x − 5)² in the Taylor series of f(x) = 1/x about a = 5.

f(x) = 1/xa = 5k = 2
c₂ =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ 0.5ᵏ/k!.

ak = 0.5ᵏ/k!
S =

Answer key

  1. 1. S6 = 0.9844
  2. 2. n = 14
  3. 3. L = 0.5437
  4. 4. L = 1.5
  5. 5. c₂ = 0.008
  6. 6. S = 1.649

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