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
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 18·(−1/3)ᵏ.

a = 18r = −1/3k₀ = 2
S =
2.Easy
kak​13579111315ε = 0.2

The geometric sequence aₙ = 5·0.8ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.2.

a₁ = 5r = 0.8ε = 0.2
n =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 2/(k(k + 2)).

ak = 2/(k(k + 2))
S =
4.Medium
AΣ 1/(4k + 7)k = 1 … ∞BΣ 1/(k(k + 4))k = 1 … ∞CΣ (3k + 1)/(k + 2)k = 1 … ∞DΣ (k + 5)/k²k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 1/(4k + 7)B: Σ 1/(k(k + 4))C: Σ (3k + 1)/(k + 2)D: Σ (k + 5)/k²
  1. 1A: Σ 1/(4k + 7)
  2. 2B: Σ 1/(k(k + 4))
  3. 3C: Σ (3k + 1)/(k + 2)
  4. 4D: Σ (k + 5)/k²
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

Recognise the series and find its sum: S = Σk=1∞ k·(−0.5)ᵏ.

ak = k·(−0.5)ᵏ
S =

Answer key

  1. 1. S = 1.5
  2. 2. n = 16
  3. 3. S = 1.5
  4. 4. B: Σ 1/(k(k + 4))
  5. 5. c₃ = −0.003906
  6. 6. S = −0.2222

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