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 = 0.1

A ball is dropped and its first rebound reaches 20 m. Every next rebound reaches 80% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 20r = 0.8ε = 0.1
n =
2.Easy
kak​12345678910

Find the sum S10 of the first 10 terms of the arithmetic sequence 6, 3, 0, −3, …

a₁ = 6d = −3n = 10
S10 =
3.Medium
kSn​12345678910

Find the sum S = Σk=125 2/(k(k + 1)).

ak = 2/(k(k + 1))n = 25
S =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 4ᵏx²ᵏ/k.

Σ 4ᵏx²ᵏ/kx₀ = 0
R =
5.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 3 at x = 1.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₃|.

f(x) = sin xn = 3x = 1.5M = 1
|R₃| =
6.Hard

Find the coefficient c₄ of (x − 2)⁴ in the Taylor series of f(x) = 1/x about a = 2.

f(x) = 1/xa = 2k = 4
c₄ =

Answer key

  1. 1. n = 25
  2. 2. S10 = −75
  3. 3. S = 1.923
  4. 4. R = 0.5
  5. 5. |R₃| = 0.2109
  6. 6. c₄ = 0.03125

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