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​123456789101112

The arithmetic sequence −7, −6.5, −6, −5.5, … ends with the term 2.5. How many terms n does it have?

a₁ = −7d = 0.5aₙ = 2.5
n =
2.Easy
kak​123456789ε = 0.1

A ball is dropped and its first rebound reaches 8 m. Every next rebound reaches 50% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 8r = 0.5ε = 0.1
n =
3.Medium
kSn​12345678910

Find the sum S = Σk=138 2/(k(k + 1)).

ak = 2/(k(k + 1))n = 38
S =
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 c₃ of (x − 4)³ in the Taylor series of f(x) = ln x about a = 4.

f(x) = ln xa = 4k = 3
c₃ =
6.Hard

f(x) = ln(1 + x) is approximated by its Maclaurin polynomial of degree 4 at x = 0.3. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 4! = 24 to find the largest possible error |R₄|.

f(x) = ln(1 + x)n = 4x = 0.3M = 24
|R₄| =

Answer key

  1. 1. n = 20
  2. 2. n = 8
  3. 3. S = 1.949
  4. 4. L = 0.3679
  5. 5. c₃ = 0.005208
  6. 6. |R₄| = 0.000486

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