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.

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1.Easy
kak​123456789101112

The arithmetic sequence −4, −3.5, −3, −2.5, … ends with the term 14.5. How many terms n does it have?

a₁ = −4d = 0.5aₙ = 14.5
n =
2.Easy
kak​123456789101112

The arithmetic sequence −12, −8, −4, 0, … ends with the term 72. How many terms n does it have?

a₁ = −12d = 4aₙ = 72
n =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ xᵏ/2ᵏ.

Σ xᵏ/2ᵏx₀ = 0
R =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ k!·xᵏ/kᵏ.

Σ k!·xᵏ/kᵏx₀ = 0
R =
5.Hard

Recognise the series and find its sum: S = Σk=0∞ 1.5ᵏ/k!.

ak = 1.5ᵏ/k!
S =
6.Hard

Find the coefficient c₂ of (x − 1)² in the Taylor series of f(x) = √x about a = 1.

f(x) = √xa = 1k = 2
c₂ =

Answer key

  1. 1. n = 38
  2. 2. n = 22
  3. 3. R = 2
  4. 4. R = 2.718
  5. 5. S = 4.482
  6. 6. c₂ = −0.125

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