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 10 m. Every next rebound reaches 75% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 10r = 0.75ε = 0.1
n =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 1, −3, 9, …

a₁ = 1r = −3n = 9
S9 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·5ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·5ᵏ/(2k)!
L =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = (k!)²·1ᵏ/(2k)!
L =
5.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·22k/(2k)!.

ak = (−1)ᵏ·22k/(2k)!
S =
6.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 2 at x = 0.2. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₂|.

f(x) = cos xn = 2x = 0.2M = 1
|R₂| =

Answer key

  1. 1. n = 18
  2. 2. S9 = 4921
  3. 3. L = 1.25
  4. 4. L = 0.25
  5. 5. S = −0.4161
  6. 6. |R₂| = 0.001333

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