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 19, 17, 15, 13, … ends with the term −7. How many terms n does it have?

a₁ = 19d = −2aₙ = −7
n =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 4·(1/4)ᵏ.

a = 4r = 1/4k₀ = 1
S =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ xᵏ/(k²·3ᵏ).

Σ xᵏ/(k²·3ᵏ)x₀ = 0
R =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 5/(k(k + 2)).

ak = 5/(k(k + 2))
S =
5.Hard
xyfP₅2.5

Use the Maclaurin polynomial of degree 5 of f(x) = sin x to approximate f(2.5). Give P₅(2.5).

f(x) = sin xn = 5x = 2.5
P₅(2.5) =
6.Hard

f(x) = eˣ 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 = e0.8 = 2.226 to find the largest possible error |R₄|.

f(x) = eˣn = 4x = 0.8M = 2.226
|R₄| =

Answer key

  1. 1. n = 14
  2. 2. S = 1.333
  3. 3. R = 3
  4. 4. S = 3.75
  5. 5. P₅(2.5) = 0.7096
  6. 6. |R₄| = 0.006077

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