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 sum S32 of the first 32 terms of the arithmetic sequence 0, 1.5, 3, 4.5, …

a₁ = 0d = 1.5n = 32
S32 =
2.Easy
kak​123456789101112ε = 0.2

The geometric sequence aₙ = 3·0.75ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.2.

a₁ = 3r = 0.75ε = 0.2
n =
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
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 16ᵏx²ᵏ/k.

Σ 16ᵏx²ᵏ/kx₀ = 0
R =
5.Hard
xyfP₃2.5

Use the Maclaurin polynomial of degree 3 of f(x) = sin(0.5x) to approximate f(2.5). Give P₃(2.5).

f(x) = sin(0.5x)n = 3x = 2.5
P₃(2.5) =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ 2ᵏ/k!.

ak = 2ᵏ/k!
S =

Answer key

  1. 1. S32 = 744
  2. 2. n = 11
  3. 3. L = 0.3679
  4. 4. R = 0.25
  5. 5. P₃(2.5) = 0.9245
  6. 6. S = 7.389

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