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​12345678

Find the sum S8 of the first 8 terms of the arithmetic sequence 0, 3, 6, 9, …

a₁ = 0d = 3n = 8
S8 =
2.Easy
kak​12345678910

Find the sum S10 of the first 10 terms of the geometric sequence 5, −15, 45, …

a₁ = 5r = −3n = 10
S10 =
3.Medium
AΣ (5/4)ᵏk = 1 … ∞BΣ k/3ᵏk = 1 … ∞CΣ 1/(k² + 8)k = 1 … ∞DΣ (3/4)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (5/4)ᵏB: Σ k/3ᵏC: Σ 1/(k² + 8)D: Σ (3/4)ᵏ
  1. 1A: Σ (5/4)ᵏ
  2. 2B: Σ k/3ᵏ
  3. 3C: Σ 1/(k² + 8)
  4. 4D: Σ (3/4)ᵏ
4.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = kᵏ/(3ᵏ·k!)
L =
5.Hard

f(x) = cos x is approximated at x = 0.5 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 1, find the smallest degree n that guarantees an error below 0.0001.

f(x) = cos xx = 0.5M = 1ε = 0.0001
n =
6.Hard
xyfP₄−1.5

Use the Maclaurin polynomial of degree 4 of f(x) = eˣ to approximate f(−1.5). Give P₄(−1.5).

f(x) = eˣn = 4x = −1.5
P₄(−1.5) =

Answer key

  1. 1. S8 = 84
  2. 2. S10 = −73810
  3. 3. A: Σ (5/4)ᵏ
  4. 4. L = 0.9061
  5. 5. n = 5
  6. 6. P₄(−1.5) = 0.2734

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