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
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 24·(1/3)ᵏ.

a = 24r = 1/3k₀ = 0
S =
2.Easy
kak​123456789101112

Find the term a36 of the arithmetic sequence −12, −7, −2, 3, …

a₁ = −12d = 5n = 36
a36 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 2)).

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

Apply the ratio test to Σk=1∞ kᵏ/(3ᵏ·k!). Find L = lim |ak+1/ak|.

ak = kᵏ/(3ᵏ·k!)
L =
5.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·0.82k+1/(2k + 1)!.

ak = (−1)ᵏ·0.82k+1/(2k + 1)!
S =
6.Hard

Find the coefficient c₃ of (x − 1)³ in the Taylor series of f(x) = ∛x about a = 1.

f(x) = ∛xa = 1k = 3
c₃ =

Answer key

  1. 1. S = 36
  2. 2. a36 = 163
  3. 3. S = 0.75
  4. 4. L = 0.9061
  5. 5. S = 0.7174
  6. 6. c₃ = 0.06173

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