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​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 1, 1.2, 1.44, …

a₁ = 1r = 1.2n = 7
S7 =
2.Easy
kak​12345

Find the sum S5 of the first 5 terms of the geometric sequence 0.5, −1, 2, …

a₁ = 0.5r = −2n = 5
S5 =
3.Medium
xx₀ = 1??R

Find the radius of convergence R of the power series Σk=1∞ k·4ᵏ·(x − 1)ᵏ.

Σ k·4ᵏ·(x − 1)ᵏx₀ = 1
R =
4.Medium
AΣ 1/k³k = 1 … ∞BΣ k³/5ᵏk = 1 … ∞CΣ (4k + 1)/(k + 2)k = 1 … ∞DΣ (1/2)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 1/k³B: Σ k³/5ᵏC: Σ (4k + 1)/(k + 2)D: Σ (1/2)ᵏ
  1. 1A: Σ 1/k³
  2. 2B: Σ k³/5ᵏ
  3. 3C: Σ (4k + 1)/(k + 2)
  4. 4D: Σ (1/2)ᵏ
5.Hard

Find the coefficient c₃ of (x − 2)³ in the Taylor series of f(x) = ln x about a = 2.

f(x) = ln xa = 2k = 3
c₃ =
6.Hard

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

ak = (−1)ᵏ/(2k)!
S =

Answer key

  1. 1. S7 = 12.92
  2. 2. S5 = 5.5
  3. 3. R = 0.25
  4. 4. C: Σ (4k + 1)/(k + 2)
  5. 5. c₃ = 0.04167
  6. 6. S = 0.5403

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