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​12345678910

Find the sum S10 of the first 10 terms of the geometric sequence 10, 15, 22.5, …

a₁ = 10r = 1.5n = 10
S10 =
2.Easy
kak​13579111315ε = 0.5

A ball is dropped and its first rebound reaches 8 m. Every next rebound reaches 85% of the previous one. Which rebound n is the first one lower than 0.5 m?

a₁ = 8r = 0.85ε = 0.5
n =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 2)).

ak = 1/(k(k + 2))
S =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 4/(k(k + 3)).

ak = 4/(k(k + 3))
S =
5.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·1.22k/(2k)!.

ak = (−1)ᵏ·1.22k/(2k)!
S =
6.Hard

Find the coefficient c₃ of (x + 1)³ in the Taylor series of f(x) = e3x about a = −1.

f(x) = e3xa = −1k = 3
c₃ =

Answer key

  1. 1. S10 = 1133
  2. 2. n = 19
  3. 3. S = 0.75
  4. 4. S = 2.444
  5. 5. S = 0.3624
  6. 6. c₃ = 0.224

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