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 = 0.2

A ball is dropped and its first rebound reaches 5 m. Every next rebound reaches 90% of the previous one. Which rebound n is the first one lower than 0.2 m?

a₁ = 5r = 0.9ε = 0.2
n =
2.Easy
kak​13579111315ε = 0.1

The geometric sequence aₙ = 20·0.75ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.1.

a₁ = 20r = 0.75ε = 0.1
n =
3.Medium
AΣ 3/k³k = 1 … ∞BΣ (3/4)ᵏk = 1 … ∞CΣ k!/3ᵏk = 1 … ∞DΣ (−1)ᵏ/√kk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 3/k³B: Σ (3/4)ᵏC: Σ k!/3ᵏD: Σ (−1)ᵏ/√k
  1. 1A: Σ 3/k³
  2. 2B: Σ (3/4)ᵏ
  3. 3C: Σ k!/3ᵏ
  4. 4D: Σ (−1)ᵏ/√k
4.Medium
xx₀ = 1??R

The power series Σk=1∞ (2k)!·(x − 1)ᵏ/(k!)² converges on an interval around x₀ = 1. Find the left end x of that interval.

Σ (2k)!·(x − 1)ᵏ/(k!)²x₀ = 1
x =
5.Hard
xyfP₂0.3

Use the Maclaurin polynomial of degree 2 of f(x) = 1/(1 + x) to approximate f(0.3). Give P₂(0.3).

f(x) = 1/(1 + x)n = 2x = 0.3
P₂(0.3) =
6.Hard
xyfP₃0.5

Use the Maclaurin polynomial of degree 3 of f(x) = ln(1 − x) to approximate f(0.5). Give P₃(0.5).

f(x) = ln(1 − x)n = 3x = 0.5
P₃(0.5) =

Answer key

  1. 1. n = 32
  2. 2. n = 20
  3. 3. C: Σ k!/3ᵏ
  4. 4. x = 0.75
  5. 5. P₂(0.3) = 0.79
  6. 6. P₃(0.5) = −0.6667

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