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 = 20·0.85ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.05.

a₁ = 20r = 0.85ε = 0.05
n =
2.Easy
kak​123456789101112

Find the term a38 of the arithmetic sequence 18, 20, 22, 24, …

a₁ = 18d = 2n = 38
a38 =
3.Medium
AΣ (−1)ᵏ/kk = 1 … ∞BΣ 2/k²k = 1 … ∞CΣ (3/4)ᵏk = 1 … ∞DΣ 3ᵏ/k³k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (−1)ᵏ/kB: Σ 2/k²C: Σ (3/4)ᵏD: Σ 3ᵏ/k³
  1. 1A: Σ (−1)ᵏ/k
  2. 2B: Σ 2/k²
  3. 3C: Σ (3/4)ᵏ
  4. 4D: Σ 3ᵏ/k³
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 4/(k(k + 1)).

ak = 4/(k(k + 1))
S =
5.Hard

Find the coefficient c₂ of (x − 4)² in the Taylor series of f(x) = √x about a = 4.

f(x) = √xa = 4k = 2
c₂ =
6.Hard

Find the coefficient c₂ of (x − 3)² in the Taylor series of f(x) = ln x about a = 3.

f(x) = ln xa = 3k = 2
c₂ =

Answer key

  1. 1. n = 38
  2. 2. a38 = 92
  3. 3. D: Σ 3ᵏ/k³
  4. 4. S = 4
  5. 5. c₂ = −0.01563
  6. 6. c₂ = −0.05556

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