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 8 m. Every next rebound reaches 90% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 8r = 0.9ε = 0.1
n =
2.Easy
kak​123456789101112

Find the sum S19 of the first 19 terms of the arithmetic sequence −12, −6, 0, 6, …

a₁ = −12d = 6n = 19
S19 =
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
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 16ᵏx²ᵏ/k.

Σ 16ᵏx²ᵏ/kx₀ = 0
R =
5.Hard

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

ak = (−1)ᵏ·22k/(2k)!
S =
6.Hard
xyfP₃0.8

Use the Maclaurin polynomial of degree 3 of f(x) = e3x to approximate f(0.8). Give P₃(0.8).

f(x) = e3xn = 3x = 0.8
P₃(0.8) =

Answer key

  1. 1. n = 43
  2. 2. S19 = 798
  3. 3. L = 1.25
  4. 4. R = 0.25
  5. 5. S = −0.4161
  6. 6. P₃(0.8) = 8.584

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