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 = 0.05

A ball is dropped and its first rebound reaches 8 m. Every next rebound reaches 90% of the previous one. Which rebound n is the first one lower than 0.05 m?

a₁ = 8r = 0.9ε = 0.05
n =
2.Easy
kak​123456789101112

Find the term a34 of the arithmetic sequence −2, −6, −10, −14, …

a₁ = −2d = −4n = 34
a34 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ 3ᵏ·k!/kᵏ. Find L = lim |ak+1/ak|.

ak = 3ᵏ·k!/kᵏ
L =
4.Medium
kSn​12345678910

Find the sum S = Σk=19 5/(k(k + 1)).

ak = 5/(k(k + 1))n = 9
S =
5.Hard

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

ak = 0.5ᵏ/k!
S =
6.Hard

Find the coefficient c₃ of (x − 1)³ in the Taylor series of f(x) = e2x about a = 1.

f(x) = e2xa = 1k = 3
c₃ =

Answer key

  1. 1. n = 50
  2. 2. a34 = −134
  3. 3. L = 1.104
  4. 4. S = 4.5
  5. 5. S = 1.649
  6. 6. c₃ = 9.852

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