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 S28 of the first 28 terms of the arithmetic sequence 13, 10, 7, 4, …

a₁ = 13d = −3n = 28
S28 =
2.Easy
kak​12345678910

Find the sum S10 of the first 10 terms of the geometric sequence 2, 1, 0.5, …

a₁ = 2r = 0.5n = 10
S10 =
3.Medium
xx₀ = −1??R

The power series Σk=1∞ k!·(x + 1)ᵏ/kᵏ converges on an interval around x₀ = −1. Find the left end x of that interval.

Σ k!·(x + 1)ᵏ/kᵏx₀ = −1
x =
4.Medium
xx₀ = 3??R

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

Σ (2k)!·(x − 3)ᵏ/(k!)²x₀ = 3
R =
5.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 =
6.Hard
xyfP₅1.2

Use the Maclaurin polynomial of degree 5 of f(x) = sin(2x) to approximate f(1.2). Give P₅(1.2).

f(x) = sin(2x)n = 5x = 1.2
P₅(1.2) =

Answer key

  1. 1. S28 = −770
  2. 2. S10 = 3.996
  3. 3. x = −3.718
  4. 4. R = 0.25
  5. 5. n = 8
  6. 6. P₅(1.2) = 0.7596

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