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 2 m. Every next rebound reaches 75% of the previous one. Which rebound n is the first one lower than 0.01 m?

a₁ = 2r = 0.75ε = 0.01
n =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 4, 3.2, 2.56, …

a₁ = 4r = 0.8n = 9
S9 =
3.Medium
AΣ 1/(k(k + 1))k = 1 … ∞BΣ k/(k + 9)k = 1 … ∞CΣ (2/5)ᵏk = 1 … ∞DΣ 3/k³k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 1/(k(k + 1))B: Σ k/(k + 9)C: Σ (2/5)ᵏD: Σ 3/k³
  1. 1A: Σ 1/(k(k + 1))
  2. 2B: Σ k/(k + 9)
  3. 3C: Σ (2/5)ᵏ
  4. 4D: Σ 3/k³
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 4ᵏx²ᵏ/k.

Σ 4ᵏx²ᵏ/kx₀ = 0
R =
5.Hard
xyfP₄0.5

Use the Maclaurin polynomial of degree 4 of f(x) = 1/(1 + x) to approximate f(0.5). Give P₄(0.5).

f(x) = 1/(1 + x)n = 4x = 0.5
P₄(0.5) =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·1.52k+1/(2k + 1)!.

ak = (−1)ᵏ·1.52k+1/(2k + 1)!
S =

Answer key

  1. 1. n = 20
  2. 2. S9 = 17.32
  3. 3. B: Σ k/(k + 9)
  4. 4. R = 0.5
  5. 5. P₄(0.5) = 0.6875
  6. 6. S = 0.9975

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