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 = 0.05

The geometric sequence aₙ = 8·0.7ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.05.

a₁ = 8r = 0.7ε = 0.05
n =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 3·(4/5)ᵏ.

a = 3r = 4/5k₀ = 1
S =
3.Medium
AΣ 5/kk = 1 … ∞BΣ k²/3ᵏk = 1 … ∞CΣ k!/2ᵏk = 1 … ∞DΣ k/(k + 9)k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 5/kB: Σ k²/3ᵏC: Σ k!/2ᵏD: Σ k/(k + 9)
  1. 1A: Σ 5/k
  2. 2B: Σ k²/3ᵏ
  3. 3C: Σ k!/2ᵏ
  4. 4D: Σ k/(k + 9)
4.Medium
AΣ k!/10ᵏk = 1 … ∞BΣ 2ᵏ/k!k = 1 … ∞CΣ 2/k⁴k = 1 … ∞DΣ (−1)ᵏ/√kk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ k!/10ᵏB: Σ 2ᵏ/k!C: Σ 2/k⁴D: Σ (−1)ᵏ/√k
  1. 1A: Σ k!/10ᵏ
  2. 2B: Σ 2ᵏ/k!
  3. 3C: Σ 2/k⁴
  4. 4D: Σ (−1)ᵏ/√k
5.Hard

Find the coefficient c₃ of (x − 4)³ in the Taylor series of f(x) = 1/x about a = 4.

f(x) = 1/xa = 4k = 3
c₃ =
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 = 16
  2. 2. S = 12
  3. 3. B: Σ k²/3ᵏ
  4. 4. A: Σ k!/10ᵏ
  5. 5. c₃ = −0.003906
  6. 6. P₃(0.8) = 8.584

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