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​135791113ε = 0.1

A ball is dropped and its first rebound reaches 20 m. Every next rebound reaches 60% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 20r = 0.6ε = 0.1
n =
2.Easy
kak​123456789101112

The arithmetic sequence 13, 13.5, 14, 14.5, … ends with the term 22.5. How many terms n does it have?

a₁ = 13d = 0.5aₙ = 22.5
n =
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
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·1ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·1ᵏ/(2k)!
L =
5.Hard

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

ak = (−2)ᵏ/k!
S =
6.Hard

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

ak = (−1)ᵏ·1.22k/(2k)!
S =

Answer key

  1. 1. n = 12
  2. 2. n = 20
  3. 3. L = 1.104
  4. 4. L = 0.25
  5. 5. S = 0.1353
  6. 6. S = 0.3624

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