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

Find the term a31 of the arithmetic sequence 1, 5, 9, 13, …

a₁ = 1d = 4n = 31
a31 =
2.Easy
kak​1234567891011

Find the sum S11 of the first 11 terms of the arithmetic sequence −5, 0, 5, 10, …

a₁ = −5d = 5n = 11
S11 =
3.Medium
k|aₖ|¹ᐟᵏ123456789101112

Apply the root test to Σk=1∞ ((2k + 2)/(4k + 6))ᵏ. Find L = lim |ak|1/k.

ak = ((2k + 2)/(4k + 6))ᵏ
L =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·3ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·3ᵏ/(2k)!
L =
5.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 3 at x = 1. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₃|.

f(x) = cos xn = 3x = 1M = 1
|R₃| =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·1.52k+1/(2k + 1)!.

ak = (−1)ᵏ·1.52k+1/(2k + 1)!
S =

Answer key

  1. 1. a31 = 121
  2. 2. S11 = 220
  3. 3. L = 0.5
  4. 4. L = 0.75
  5. 5. |R₃| = 0.04167
  6. 6. S = 0.9975

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