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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
kak​13579111315ε = 0.01

A ball is dropped and its first rebound reaches 5 m. Every next rebound reaches 80% of the previous one. Which rebound n is the first one lower than 0.01 m?

a₁ = 5r = 0.8ε = 0.01
n =
2.Easy
kak​123456789101112

Find the term a21 of the arithmetic sequence −12, −9.5, −7, −4.5, …

a₁ = −12d = 2.5n = 21
a21 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 5/(k(k + 1)).

ak = 5/(k(k + 1))
S =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = kᵏ/(3ᵏ·k!)
L =
5.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·0.82k+1/(2k + 1)!.

ak = (−1)ᵏ·0.82k+1/(2k + 1)!
S =
6.Hard

Find the coefficient c₂ of (x − 4)² in the Taylor series of f(x) = ln x about a = 4.

f(x) = ln xa = 4k = 2
c₂ =

Answer key

  1. 1. n = 29
  2. 2. a21 = 38
  3. 3. S = 5
  4. 4. L = 0.9061
  5. 5. S = 0.7174
  6. 6. c₂ = −0.03125

Full step-by-step solutions: practise this topic on examproblems.com.