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

A ball is dropped and its first rebound reaches 10 m. Every next rebound reaches 70% of the previous one. Which rebound n is the first one lower than 0.01 m?

a₁ = 10r = 0.7ε = 0.01
n =
2.Easy
kak​123456789

The arithmetic sequence −2, −6, −10, −14, … ends with the term −34. How many terms n does it have?

a₁ = −2d = −4aₙ = −34
n =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 12/(k(k + 2)).

ak = 12/(k(k + 2))
S =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ 3ᵏ·k!/kᵏ. Find L = lim |ak+1/ak|.

ak = 3ᵏ·k!/kᵏ
L =
5.Hard

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

f(x) = ln xa = 2k = 2
c₂ =
6.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 =

Answer key

  1. 1. n = 21
  2. 2. n = 9
  3. 3. S = 9
  4. 4. L = 1.104
  5. 5. c₂ = −0.125
  6. 6. n = 10

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