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​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 2, 4, 8, …

a₁ = 2r = 2n = 7
S7 =
2.Easy
kak​13579111315ε = 0.05

The geometric sequence aₙ = 3·0.8ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.05.

a₁ = 3r = 0.8ε = 0.05
n =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 12/(k(k + 4)).

ak = 12/(k(k + 4))
S =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 12/(k(k + 3)).

ak = 12/(k(k + 3))
S =
5.Hard

Find the coefficient c₄ of (x − 2)⁴ in the Taylor series of f(x) = 1/x about a = 2.

f(x) = 1/xa = 2k = 4
c₄ =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·0.52k+1/(2k + 1)!.

ak = (−1)ᵏ·0.52k+1/(2k + 1)!
S =

Answer key

  1. 1. S7 = 254
  2. 2. n = 20
  3. 3. S = 6.25
  4. 4. S = 7.333
  5. 5. c₄ = 0.03125
  6. 6. S = 0.4794

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