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​123456789101112

The arithmetic sequence −2, 0, 2, 4, … ends with the term 48. How many terms n does it have?

a₁ = −2d = 2aₙ = 48
n =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 6·(−1/3)ᵏ.

a = 6r = −1/3k₀ = 2
S =
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 = 0??R

Find the radius of convergence R of the power series Σk=1∞ xᵏ/(k²·2ᵏ).

Σ xᵏ/(k²·2ᵏ)x₀ = 0
R =
5.Hard

f(x) = cos x is approximated at x = 0.5 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 1, find the smallest degree n that guarantees an error below 0.0005.

f(x) = cos xx = 0.5M = 1ε = 0.0005
n =
6.Hard

Find the coefficient c₄ of (x − 3)⁴ in the Taylor series of f(x) = 1/x about a = 3.

f(x) = 1/xa = 3k = 4
c₄ =

Answer key

  1. 1. n = 26
  2. 2. S = 0.5
  3. 3. L = 1.25
  4. 4. R = 2
  5. 5. n = 4
  6. 6. c₄ = 0.004115

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