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​12345

Find the sum S5 of the first 5 terms of the geometric sequence 5, −15, 45, …

a₁ = 5r = −3n = 5
S5 =
2.Easy
kak​13579111315ε = 0.01

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 0.01 m?

a₁ = 8r = 0.75ε = 0.01
n =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = (k!)²·5ᵏ/(2k)!
L =
4.Medium
xx₀ = 2??R

The power series Σk=1∞ (x − 2)ᵏ/(k·2ᵏ) converges on an interval around x₀ = 2. Find the right end x of that interval.

Σ (x − 2)ᵏ/(k·2ᵏ)x₀ = 2
x =
5.Hard

Find the coefficient c₄ of (x − 1)⁴ in the Taylor series of f(x) = √x about a = 1.

f(x) = √xa = 1k = 4
c₄ =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ 1.5ᵏ/k!.

ak = 1.5ᵏ/k!
S =

Answer key

  1. 1. S5 = 305
  2. 2. n = 25
  3. 3. L = 1.25
  4. 4. x = 4
  5. 5. c₄ = −0.03906
  6. 6. S = 4.482

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