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 = 3·0.85ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.05.

a₁ = 3r = 0.85ε = 0.05
n =
2.Easy
kak​123456789101112

The arithmetic sequence −7, −6.5, −6, −5.5, … ends with the term 2.5. How many terms n does it have?

a₁ = −7d = 0.5aₙ = 2.5
n =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k·3ᵏ/4ᵏ. Find L = lim |ak+1/ak|.

ak = k·3ᵏ/4ᵏ
L =
4.Medium
AΣ (−1)ᵏ/kk = 1 … ∞BΣ (4k + 1)/(k + 2)k = 1 … ∞CΣ 2ᵏ/k²k = 1 … ∞DΣ 1/√kk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (−1)ᵏ/kB: Σ (4k + 1)/(k + 2)C: Σ 2ᵏ/k²D: Σ 1/√k
  1. 1A: Σ (−1)ᵏ/k
  2. 2B: Σ (4k + 1)/(k + 2)
  3. 3C: Σ 2ᵏ/k²
  4. 4D: Σ 1/√k
5.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) =
6.Hard
xyfP₃0.5

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

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

Answer key

  1. 1. n = 27
  2. 2. n = 20
  3. 3. L = 0.75
  4. 4. A: Σ (−1)ᵏ/k
  5. 5. P₃(0.5) = 0.4167
  6. 6. P₃(0.5) = 1.875

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