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​123456789101112

Find the sum S25 of the first 25 terms of the arithmetic sequence −9, −12, −15, −18, …

a₁ = −9d = −3n = 25
S25 =
2.Easy
kak​13579111315ε = 0.01

The geometric sequence aₙ = 5·0.7ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.01.

a₁ = 5r = 0.7ε = 0.01
n =
3.Medium
xx₀ = 2??R

Find the radius of convergence R of the power series Σk=1∞ k·3ᵏ·(x − 2)ᵏ.

Σ k·3ᵏ·(x − 2)ᵏx₀ = 2
R =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 2/(k(k + 3)).

ak = 2/(k(k + 3))
S =
5.Hard

Find the coefficient c₄ of (x − 1)⁴ in the Taylor series of f(x) = ∛x about a = 1.

f(x) = ∛xa = 1k = 4
c₄ =
6.Hard

f(x) = cos x is approximated at x = 1.5 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 1, find the smallest degree n that guarantees an error below 1 × 10⁻⁶.

f(x) = cos xx = 1.5M = 1ε = 1 × 10⁻⁶
n =

Answer key

  1. 1. S25 = −1125
  2. 2. n = 19
  3. 3. R = 0.3333
  4. 4. S = 1.222
  5. 5. c₄ = −0.04115
  6. 6. n = 11

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