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​12345678910

Find the sum S10 of the first 10 terms of the arithmetic sequence 13, 9, 5, 1, …

a₁ = 13d = −4n = 10
S10 =
2.Easy
kak​12345

Find the sum S5 of the first 5 terms of the geometric sequence 2, 6, 18, …

a₁ = 2r = 3n = 5
S5 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

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

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

Find the sum S = Σk=134 4/(k(k + 1)).

ak = 4/(k(k + 1))n = 34
S =
5.Hard

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

ak = (−1)ᵏ/k!
S =
6.Hard
xyfP₂1

Use the Maclaurin polynomial of degree 2 of f(x) = cos x to approximate f(1). Give P₂(1).

f(x) = cos xn = 2x = 1
P₂(1) =

Answer key

  1. 1. S10 = −50
  2. 2. S5 = 242
  3. 3. L = 0.5
  4. 4. S = 3.886
  5. 5. S = 0.3679
  6. 6. P₂(1) = 0.5

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