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​13579111315ε = 0.01

The geometric sequence aₙ = 3·0.8ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.01.

a₁ = 3r = 0.8ε = 0.01
n =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 4, 3.2, 2.56, …

a₁ = 4r = 0.8n = 9
S9 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 6/(k(k + 3)).

ak = 6/(k(k + 3))
S =
4.Medium
xx₀ = 2??R

The power series Σk=1∞ (2k)!·(x − 2)ᵏ/(k!)² converges on an interval around x₀ = 2. Find the left end x of that interval.

Σ (2k)!·(x − 2)ᵏ/(k!)²x₀ = 2
x =
5.Hard

f(x) = eˣ is approximated at x = 2 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 8, find the smallest degree n that guarantees an error below 0.0005.

f(x) = eˣx = 2M = 8ε = 0.0005
n =
6.Hard

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

ak = (−1)ᵏ·0.52k/(2k)!
S =

Answer key

  1. 1. n = 27
  2. 2. S9 = 17.32
  3. 3. S = 3.667
  4. 4. x = 1.75
  5. 5. n = 10
  6. 6. S = 0.8776

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