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​12345

Find the sum S5 of the first 5 terms of the geometric sequence 0.5, 1.5, 4.5, …

a₁ = 0.5r = 3n = 5
S5 =
2.Easy
kak​12345678910ε = 0.05

The geometric sequence aₙ = 2·0.6ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.05.

a₁ = 2r = 0.6ε = 0.05
n =
3.Medium
AΣ 3ᵏ/k²k = 1 … ∞BΣ 1/k²k = 1 … ∞CΣ 10ᵏ/k!k = 1 … ∞DΣ 1/(k(k + 2))k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 3ᵏ/k²B: Σ 1/k²C: Σ 10ᵏ/k!D: Σ 1/(k(k + 2))
  1. 1A: Σ 3ᵏ/k²
  2. 2B: Σ 1/k²
  3. 3C: Σ 10ᵏ/k!
  4. 4D: Σ 1/(k(k + 2))
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) = ln x about a = 4.

f(x) = ln xa = 4k = 2
c₂ =
6.Hard
xyfP₃0.8

Use the Maclaurin polynomial of degree 3 of f(x) = e−x to approximate f(0.8). Give P₃(0.8).

f(x) = e−xn = 3x = 0.8
P₃(0.8) =

Answer key

  1. 1. S5 = 60.5
  2. 2. n = 9
  3. 3. A: Σ 3ᵏ/k²
  4. 4. S = 4
  5. 5. c₂ = −0.03125
  6. 6. P₃(0.8) = 0.4347

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