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​123456789101112

Find the sum S30 of the first 30 terms of the arithmetic sequence 1, 6, 11, 16, …

a₁ = 1d = 5n = 30
S30 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 8·(−1/2)ᵏ.

a = 8r = −1/2k₀ = 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∞ 5/(k(k + 3)).

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

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

ak = (−1)ᵏ/(2k)!
S =
6.Hard

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

ak = 2ᵏ/k!
S =

Answer key

  1. 1. S30 = 2205
  2. 2. S = −2.667
  3. 3. L = 1.25
  4. 4. S = 3.056
  5. 5. S = 0.5403
  6. 6. S = 7.389

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