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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Name: ____________________   Date: ____________

1.Easy
kak​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 4, 2, 1, …

a₁ = 4r = 0.5n = 7
S7 =
2.Easy
kak​13579111315ε = 0.1

The geometric sequence aₙ = 2·0.85ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.1.

a₁ = 2r = 0.85ε = 0.1
n =
3.Medium
AΣ 3/k³k = 1 … ∞BΣ 3ᵏ/k³k = 1 … ∞CΣ (k + 3)/k²k = 1 … ∞DΣ (3/2)ᵏk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 3/k³B: Σ 3ᵏ/k³C: Σ (k + 3)/k²D: Σ (3/2)ᵏ
  1. 1A: Σ 3/k³
  2. 2B: Σ 3ᵏ/k³
  3. 3C: Σ (k + 3)/k²
  4. 4D: Σ (3/2)ᵏ
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·5ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·5ᵏ/(2k)!
L =
5.Hard
xyfP₃0.25

Use the Maclaurin polynomial of degree 3 of f(x) = ln(1 + 2x) to approximate f(0.25). Give P₃(0.25).

f(x) = ln(1 + 2x)n = 3x = 0.25
P₃(0.25) =
6.Hard

Find the coefficient c₂ of (x − 1)² in the Taylor series of f(x) = ∛x about a = 1.

f(x) = ∛xa = 1k = 2
c₂ =

Answer key

  1. 1. S7 = 7.938
  2. 2. n = 20
  3. 3. A: Σ 3/k³
  4. 4. L = 1.25
  5. 5. P₃(0.25) = 0.4167
  6. 6. c₂ = −0.1111

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