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
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 9·(3/4)ᵏ.

a = 9r = 3/4k₀ = 2
S =
2.Easy
kak​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 1, −2, 4, …

a₁ = 1r = −2n = 7
S7 =
3.Medium
k|aₖ|¹ᐟᵏ123456789101112

Apply the root test to Σk=1∞ ((1k + 6)/(2k + 3))ᵏ. Find L = lim |ak|1/k.

ak = ((1k + 6)/(2k + 3))ᵏ
L =
4.Medium
kSn​12345678910

Find the sum S = Σk=15 3/(k(k + 1)).

ak = 3/(k(k + 1))n = 5
S =
5.Hard

Find the coefficient c₂ of (x − 1)² in the Taylor series of f(x) = √x about a = 1.

f(x) = √xa = 1k = 2
c₂ =
6.Hard

Find the coefficient c₃ of (x − 1)³ in the Taylor series of f(x) = e3x about a = 1.

f(x) = e3xa = 1k = 3
c₃ =

Answer key

  1. 1. S = 20.25
  2. 2. S7 = 43
  3. 3. L = 0.5
  4. 4. S = 2.5
  5. 5. c₂ = −0.125
  6. 6. c₃ = 90.38

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