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​12345678

Find the sum S8 of the first 8 terms of the geometric sequence 3, 2.4, 1.92, …

a₁ = 3r = 0.8n = 8
S8 =
2.Easy
kak​1234567891011ε = 0.1

The geometric sequence aₙ = 8·0.6ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.1.

a₁ = 8r = 0.6ε = 0.1
n =
3.Medium
xx₀ = 0??R

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

Σ k·2ᵏ·xᵏx₀ = 0
R =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 4/(k(k + 2)).

ak = 4/(k(k + 2))
S =
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

f(x) = cos x is approximated at x = 2 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 1, find the smallest degree n that guarantees an error below 0.001.

f(x) = cos xx = 2M = 1ε = 0.001
n =

Answer key

  1. 1. S8 = 12.48
  2. 2. n = 10
  3. 3. R = 0.5
  4. 4. S = 3
  5. 5. c₃ = 0.04167
  6. 6. n = 9

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