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

The geometric sequence aₙ = 20·0.9ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.2.

a₁ = 20r = 0.9ε = 0.2
n =
2.Easy
kak​1234567891011

Find the sum S11 of the first 11 terms of the arithmetic sequence 2, 6, 10, 14, …

a₁ = 2d = 4n = 11
S11 =
3.Medium
AΣ k²/3ᵏk = 1 … ∞BΣ 2/k²k = 1 … ∞CΣ 1/(k(k + 4))k = 1 … ∞DΣ ln k / kk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ k²/3ᵏB: Σ 2/k²C: Σ 1/(k(k + 4))D: Σ ln k / k
  1. 1A: Σ k²/3ᵏ
  2. 2B: Σ 2/k²
  3. 3C: Σ 1/(k(k + 4))
  4. 4D: Σ ln k / k
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 5/(k(k + 1)).

ak = 5/(k(k + 1))
S =
5.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 2 at x = 0.3. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₂|.

f(x) = sin xn = 2x = 0.3M = 1
|R₂| =
6.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 5 at x = 0.8. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e0.8 = 2.226 to find the largest possible error |R₅|.

f(x) = eˣn = 5x = 0.8M = 2.226
|R₅| =

Answer key

  1. 1. n = 45
  2. 2. S11 = 242
  3. 3. D: Σ ln k / k
  4. 4. S = 5
  5. 5. |R₂| = 0.0045
  6. 6. |R₅| = 0.0008103

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