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 −10, −12, −14, −16, … ends with the term −32. How many terms n does it have?

a₁ = −10d = −2aₙ = −32
n =
2.Easy
kak​13579111315ε = 0.5

The geometric sequence aₙ = 20·0.85ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.5.

a₁ = 20r = 0.85ε = 0.5
n =
3.Medium
k|aₖ|¹ᐟᵏ123456789101112

Apply the root test to Σk=1∞ ((4k + 1)/(6k + 3))ᵏ. Find L = lim |ak|1/k.

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

Find the sum S = Σk=1∞ 6/(k(k + 4)).

ak = 6/(k(k + 4))
S =
5.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 4 at x = 0.8. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₄|.

f(x) = sin xn = 4x = 0.8M = 1
|R₄| =
6.Hard

Find the coefficient c₂ of (x − 16)² in the Taylor series of f(x) = √x about a = 16.

f(x) = √xa = 16k = 2
c₂ =

Answer key

  1. 1. n = 12
  2. 2. n = 24
  3. 3. L = 0.6667
  4. 4. S = 3.125
  5. 5. |R₄| = 0.002731
  6. 6. c₂ = −0.001953

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