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 S19 of the first 19 terms of the arithmetic sequence 7, 4, 1, −2, …

a₁ = 7d = −3n = 19
S19 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 12·(1/4)ᵏ.

a = 12r = 1/4k₀ = 0
S =
3.Medium
xx₀ = 3??R

Find the radius of convergence R of the power series Σk=1∞ 5ᵏ·(x − 3)ᵏ/(k + 1).

Σ 5ᵏ·(x − 3)ᵏ/(k + 1)x₀ = 3
R =
4.Medium
AΣ 1/(k² + 2)k = 1 … ∞BΣ (4/5)ᵏk = 1 … ∞CΣ k³/3ᵏk = 1 … ∞DΣ 1/(3k + 1)k = 1 … ∞

Exactly one of the four series diverges. Click it.

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

Find the coefficient c₄ of (x − 1)⁴ in the Taylor series of f(x) = ln x about a = 1.

f(x) = ln xa = 1k = 4
c₄ =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·0.52k+1/(2k + 1)!.

ak = (−1)ᵏ·0.52k+1/(2k + 1)!
S =

Answer key

  1. 1. S19 = −380
  2. 2. S = 16
  3. 3. R = 0.2
  4. 4. D: Σ 1/(3k + 1)
  5. 5. c₄ = −0.25
  6. 6. S = 0.4794

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