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

The arithmetic sequence −2, 0, 2, 4, … ends with the term 38. How many terms n does it have?

a₁ = −2d = 2aₙ = 38
n =
2.Easy
kak​123456789101112

Find the term a30 of the arithmetic sequence 14, 10, 6, 2, …

a₁ = 14d = −4n = 30
a30 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 6/(k(k + 3)).

ak = 6/(k(k + 3))
S =
4.Medium
xx₀ = 3??R

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

Σ k·2ᵏ·(x − 3)ᵏx₀ = 3
R =
5.Hard

f(x) = sin x is approximated at x = 2 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 0.001.

f(x) = sin xx = 2M = 1ε = 0.001
n =
6.Hard
xyfP₃0.5

Use the Maclaurin polynomial of degree 3 of f(x) = 1/(1 − x) to approximate f(0.5). Give P₃(0.5).

f(x) = 1/(1 − x)n = 3x = 0.5
P₃(0.5) =

Answer key

  1. 1. n = 21
  2. 2. a30 = −102
  3. 3. S = 3.667
  4. 4. R = 0.5
  5. 5. n = 9
  6. 6. P₃(0.5) = 1.875

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