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 70% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 20r = 0.7ε = 0.1
n =
2.Easy
kak​123456789101112

The arithmetic sequence 11, 12.5, 14, 15.5, … ends with the term 66.5. How many terms n does it have?

a₁ = 11d = 1.5aₙ = 66.5
n =
3.Medium
AΣ k/2ᵏk = 1 … ∞BΣ 1/(k(k + 2))k = 1 … ∞CΣ 5/k³k = 1 … ∞DΣ (7/4)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ k/2ᵏB: Σ 1/(k(k + 2))C: Σ 5/k³D: Σ (7/4)ᵏ
  1. 1A: Σ k/2ᵏ
  2. 2B: Σ 1/(k(k + 2))
  3. 3C: Σ 5/k³
  4. 4D: Σ (7/4)ᵏ
4.Medium
k|aₖ|¹ᐟᵏ123456789101112

Apply the root test to Σk=1∞ ((5k + 3)/(3k + 1))ᵏ. Find L = lim |ak|1/k.

ak = ((5k + 3)/(3k + 1))ᵏ
L =
5.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 3 at x = 0.3. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₃|.

f(x) = cos xn = 3x = 0.3M = 1
|R₃| =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·1.22k/(2k)!.

ak = (−1)ᵏ·1.22k/(2k)!
S =

Answer key

  1. 1. n = 16
  2. 2. n = 38
  3. 3. D: Σ (7/4)ᵏ
  4. 4. L = 1.667
  5. 5. |R₃| = 0.0003375
  6. 6. S = 0.3624

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