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​12345678910ε = 0.1

A ball is dropped and its first rebound reaches 5 m. Every next rebound reaches 60% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 5r = 0.6ε = 0.1
n =
2.Easy
kak​123456789101112

Find the sum S15 of the first 15 terms of the arithmetic sequence 16, 18, 20, 22, …

a₁ = 16d = 2n = 15
S15 =
3.Medium
xx₀ = 2??R

Find the radius of convergence R of the power series Σk=1∞ (x − 2)ᵏ/(1/2)ᵏ.

Σ (x − 2)ᵏ/(1/2)ᵏx₀ = 2
R =
4.Medium
AΣ 1/√kk = 1 … ∞BΣ 2ᵏ/k²k = 1 … ∞CΣ (7/4)ᵏk = 1 … ∞DΣ 1/k⁴k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 1/√kB: Σ 2ᵏ/k²C: Σ (7/4)ᵏD: Σ 1/k⁴
  1. 1A: Σ 1/√k
  2. 2B: Σ 2ᵏ/k²
  3. 3C: Σ (7/4)ᵏ
  4. 4D: Σ 1/k⁴
5.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 2 at x = 0.3. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e0.3 = 1.35 to find the largest possible error |R₂|.

f(x) = eˣn = 2x = 0.3M = 1.35
|R₂| =
6.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 4 at x = 0.5. 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 = 0.5M = 1
|R₄| =

Answer key

  1. 1. n = 9
  2. 2. S15 = 450
  3. 3. R = 0.5
  4. 4. D: Σ 1/k⁴
  5. 5. |R₂| = 0.006074
  6. 6. |R₄| = 0.0002604

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