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 −5, −1, 3, 7, … ends with the term 67. How many terms n does it have?

a₁ = −5d = 4aₙ = 67
n =
2.Easy
kak​123456789101112

The arithmetic sequence 8, 14, 20, 26, … ends with the term 170. How many terms n does it have?

a₁ = 8d = 6aₙ = 170
n =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 12/(k(k + 4)).

ak = 12/(k(k + 4))
S =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k³·3ᵏ/4ᵏ. Find L = lim |ak+1/ak|.

ak = k³·3ᵏ/4ᵏ
L =
5.Hard

f(x) = cos x is approximated at x = 1.5 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 0.001.

f(x) = cos xx = 1.5M = 1ε = 0.001
n =
6.Hard

f(x) = cos x is approximated at x = 1.5 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 = 1.5M = 1ε = 0.0005
n =

Answer key

  1. 1. n = 19
  2. 2. n = 28
  3. 3. S = 6.25
  4. 4. L = 0.75
  5. 5. n = 7
  6. 6. n = 8

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