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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Name: ____________________   Date: ____________

1.Easy
kak​123456789101112

Find the term a15 of the arithmetic sequence −4, 0, 4, 8, …

a₁ = −4d = 4n = 15
a15 =
2.Easy
kak​12345678910

Find the sum S10 of the first 10 terms of the geometric sequence 2, −4, 8, …

a₁ = 2r = −2n = 10
S10 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 4/(k(k + 3)).

ak = 4/(k(k + 3))
S =
4.Medium
xx₀ = 0??R

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

Σ (2k)!·xᵏ/(k!)²x₀ = 0
R =
5.Hard

Recognise the series and find its sum: S = Σk=1∞ k·0.25ᵏ.

ak = k·0.25ᵏ
S =
6.Hard

f(x) = sin x is approximated at x = 1 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 = 1M = 1ε = 0.0005
n =

Answer key

  1. 1. a15 = 52
  2. 2. S10 = −682
  3. 3. S = 2.444
  4. 4. R = 0.25
  5. 5. S = 0.4444
  6. 6. n = 6

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