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 = 0.05

A ball is dropped and its first rebound reaches 20 m. Every next rebound reaches 85% of the previous one. Which rebound n is the first one lower than 0.05 m?

a₁ = 20r = 0.85ε = 0.05
n =
2.Easy
kak​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 2, 6, 18, …

a₁ = 2r = 3n = 7
S7 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ kᵏ/(2ᵏ·k!). Find L = lim |ak+1/ak|.

ak = kᵏ/(2ᵏ·k!)
L =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k!/kᵏ. Find L = lim |ak+1/ak|.

ak = k!/kᵏ
L =
5.Hard

Find the coefficient c₄ of (x − 2)⁴ in the Taylor series of f(x) = ln x about a = 2.

f(x) = ln xa = 2k = 4
c₄ =
6.Hard

f(x) = sin x is approximated at x = 0.5 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 0.0001.

f(x) = sin xx = 0.5M = 1ε = 0.0001
n =

Answer key

  1. 1. n = 38
  2. 2. S7 = 2186
  3. 3. L = 1.359
  4. 4. L = 0.3679
  5. 5. c₄ = −0.01563
  6. 6. n = 5

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