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 2, −6, 18, …

a₁ = 2r = −3n = 6
S6 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 10·(1/3)ᵏ.

a = 10r = 1/3k₀ = 1
S =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 6/(k(k + 3)).

ak = 6/(k(k + 3))
S =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 2/(k(k + 3)).

ak = 2/(k(k + 3))
S =
5.Hard

Recognise the series and find its sum: S = Σk=0∞ 3ᵏ/k!.

ak = 3ᵏ/k!
S =
6.Hard

f(x) = cos 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 1 × 10⁻⁶.

f(x) = cos xx = 1M = 1ε = 1 × 10⁻⁶
n =

Answer key

  1. 1. S6 = −364
  2. 2. S = 5
  3. 3. S = 3.667
  4. 4. S = 1.222
  5. 5. S = 20.09
  6. 6. n = 9

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