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 0.5, −0.25, 0.125, …

a₁ = 0.5r = −0.5n = 6
S6 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 2·(3/4)ᵏ.

a = 2r = 3/4k₀ = 0
S =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 6/(k(k + 3)).

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

Find the sum S = Σk=16 12/(k(k + 1)).

ak = 12/(k(k + 1))n = 6
S =
5.Hard

Find the coefficient c₂ of (x − 4)² in the Taylor series of f(x) = √x about a = 4.

f(x) = √xa = 4k = 2
c₂ =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·22k/(2k)!.

ak = (−1)ᵏ·22k/(2k)!
S =

Answer key

  1. 1. S6 = 0.3281
  2. 2. S = 8
  3. 3. S = 3.667
  4. 4. S = 10.29
  5. 5. c₂ = −0.01563
  6. 6. S = −0.4161

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