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​123456

Find the sum S6 of the first 6 terms of the geometric sequence 10, −30, 90, …

a₁ = 10r = −3n = 6
S6 =
2.Easy
kak​123456789101112

The arithmetic sequence 16, 14, 12, 10, … ends with the term −52. How many terms n does it have?

a₁ = 16d = −2aₙ = −52
n =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ (1/2)ᵏ·xᵏ/(k + 1).

Σ (1/2)ᵏ·xᵏ/(k + 1)x₀ = 0
R =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ 3ᵏ·k!/kᵏ. Find L = lim |ak+1/ak|.

ak = 3ᵏ·k!/kᵏ
L =
5.Hard

Recognise the series and find its sum: S = Σk=1∞ k·(1/3)ᵏ.

ak = k·(1/3)ᵏ
S =
6.Hard

f(x) = sin 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 0.0005.

f(x) = sin xx = 1.5M = 1ε = 0.0005
n =

Answer key

  1. 1. S6 = −1820
  2. 2. n = 35
  3. 3. R = 2
  4. 4. L = 1.104
  5. 5. S = 0.75
  6. 6. n = 8

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