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 2, 1, 0.5, …

a₁ = 2r = 0.5n = 5
S5 =
2.Easy
kak​12345678910ε = 0.2

The geometric sequence aₙ = 8·0.6ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.2.

a₁ = 8r = 0.6ε = 0.2
n =
3.Medium
kSn​12345678910

Find the sum S = Σk=117 5/(k(k + 1)).

ak = 5/(k(k + 1))n = 17
S =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ k!·xᵏ/kᵏ.

Σ k!·xᵏ/kᵏx₀ = 0
R =
5.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 4 at x = 1.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₄|.

f(x) = sin xn = 4x = 1.5M = 1
|R₄| =
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. S5 = 3.875
  2. 2. n = 9
  3. 3. S = 4.722
  4. 4. R = 2.718
  5. 5. |R₄| = 0.06328
  6. 6. c₂ = −0.1111

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