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
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 12·(2/5)ᵏ.

a = 12r = 2/5k₀ = 1
S =
2.Easy
kak​123456789101112

Find the sum S15 of the first 15 terms of the arithmetic sequence 7, 9, 11, 13, …

a₁ = 7d = 2n = 15
S15 =
3.Medium
AΣ (3k + 1)/(k + 2)k = 1 … ∞BΣ ln k / kk = 1 … ∞CΣ (3/2)ᵏk = 1 … ∞DΣ k²/2ᵏk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (3k + 1)/(k + 2)B: Σ ln k / kC: Σ (3/2)ᵏD: Σ k²/2ᵏ
  1. 1A: Σ (3k + 1)/(k + 2)
  2. 2B: Σ ln k / k
  3. 3C: Σ (3/2)ᵏ
  4. 4D: Σ k²/2ᵏ
4.Medium
AΣ (2/3)ᵏk = 1 … ∞BΣ k³/2ᵏk = 1 … ∞CΣ 2/k⁴k = 1 … ∞DΣ 2ᵏ/k²k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (2/3)ᵏB: Σ k³/2ᵏC: Σ 2/k⁴D: Σ 2ᵏ/k²
  1. 1A: Σ (2/3)ᵏ
  2. 2B: Σ k³/2ᵏ
  3. 3C: Σ 2/k⁴
  4. 4D: Σ 2ᵏ/k²
5.Hard

f(x) = ln(1 + x) is approximated by its Maclaurin polynomial of degree 5 at x = 0.2. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 5! = 120 to find the largest possible error |R₅|.

f(x) = ln(1 + x)n = 5x = 0.2M = 120
|R₅| =
6.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 2 at x = 1.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₂|.

f(x) = sin xn = 2x = 1.5M = 1
|R₂| =

Answer key

  1. 1. S = 8
  2. 2. S15 = 315
  3. 3. D: Σ k²/2ᵏ
  4. 4. D: Σ 2ᵏ/k²
  5. 5. |R₅| = 1.067 × 10⁻⁵
  6. 6. |R₂| = 0.5625

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