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​123456

Find the sum S6 of the first 6 terms of the geometric sequence 5, 4, 3.2, …

a₁ = 5r = 0.8n = 6
S6 =
2.Easy
kak​123456789101112

Find the term a38 of the arithmetic sequence 6, 7.5, 9, 10.5, …

a₁ = 6d = 1.5n = 38
a38 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = k!/kᵏ
L =
4.Medium
kSn​12345678910

Find the sum S = Σk=126 5/(k(k + 1)).

ak = 5/(k(k + 1))n = 26
S =
5.Hard

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

ak = (−1)ᵏ·1.22k/(2k)!
S =
6.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 5 at x = 0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₅|.

f(x) = sin xn = 5x = 0.5M = 1
|R₅| =

Answer key

  1. 1. S6 = 18.45
  2. 2. a38 = 61.5
  3. 3. L = 0.3679
  4. 4. S = 4.815
  5. 5. S = 0.3624
  6. 6. |R₅| = 2.17 × 10⁻⁵

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