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​123456789101112

Find the sum S37 of the first 37 terms of the arithmetic sequence −9, −7, −5, −3, …

a₁ = −9d = 2n = 37
S37 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 10·(3/4)ᵏ.

a = 10r = 3/4k₀ = 1
S =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·5ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·5ᵏ/(2k)!
L =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 12/(k(k + 3)).

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

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

ak = (−1)ᵏ·0.52k/(2k)!
S =
6.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 =

Answer key

  1. 1. S37 = 999
  2. 2. S = 30
  3. 3. L = 1.25
  4. 4. S = 7.333
  5. 5. S = 0.8776
  6. 6. c₂ = −0.01563

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