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 a17 of the arithmetic sequence 11, 16, 21, 26, …

a₁ = 11d = 5n = 17
a17 =
2.Easy
kak​13579111315ε = 0.1

The geometric sequence aₙ = 8·0.75ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.1.

a₁ = 8r = 0.75ε = 0.1
n =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 2/(k(k + 3)).

ak = 2/(k(k + 3))
S =
4.Medium
xx₀ = 1??R

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

Σ k!·(x − 1)ᵏ/kᵏx₀ = 1
R =
5.Hard

f(x) = eˣ is approximated at x = 2 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 8, find the smallest degree n that guarantees an error below 1 × 10⁻⁵.

f(x) = eˣx = 2M = 8ε = 1 × 10⁻⁵
n =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·1.22k/(2k)!.

ak = (−1)ᵏ·1.22k/(2k)!
S =

Answer key

  1. 1. a17 = 91
  2. 2. n = 17
  3. 3. S = 1.222
  4. 4. R = 2.718
  5. 5. n = 13
  6. 6. S = 0.3624

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