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​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 1, −0.5, 0.25, …

a₁ = 1r = −0.5n = 9
S9 =
2.Easy
kak​12345678910

Find the term a10 of the arithmetic sequence 5, 6.5, 8, 9.5, …

a₁ = 5d = 1.5n = 10
a10 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 4/(k(k + 2)).

ak = 4/(k(k + 2))
S =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·1ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·1ᵏ/(2k)!
L =
5.Hard

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

ak = (−1)ᵏ/(2k)!
S =
6.Hard

Find the coefficient c₄ of (x + 1)⁴ in the Taylor series of f(x) = e3x about a = −1.

f(x) = e3xa = −1k = 4
c₄ =

Answer key

  1. 1. S9 = 0.668
  2. 2. a10 = 18.5
  3. 3. S = 3
  4. 4. L = 0.25
  5. 5. S = 0.5403
  6. 6. c₄ = 0.168

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