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​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 2, 2.4, 2.88, …

a₁ = 2r = 1.2n = 7
S7 =
2.Easy
kak​123456

Find the sum S6 of the first 6 terms of the geometric sequence 5, 7.5, 11.25, …

a₁ = 5r = 1.5n = 6
S6 =
3.Medium
AΣ (1 + 1/k)ᵏk = 1 … ∞BΣ 3ᵏ/k²k = 1 … ∞CΣ 1/(2k + 1)k = 1 … ∞DΣ (1/2)ᵏk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (1 + 1/k)ᵏB: Σ 3ᵏ/k²C: Σ 1/(2k + 1)D: Σ (1/2)ᵏ
  1. 1A: Σ (1 + 1/k)ᵏ
  2. 2B: Σ 3ᵏ/k²
  3. 3C: Σ 1/(2k + 1)
  4. 4D: Σ (1/2)ᵏ
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/k!.

ak = (−1)ᵏ/k!
S =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ 0.5ᵏ/k!.

ak = 0.5ᵏ/k!
S =

Answer key

  1. 1. S7 = 25.83
  2. 2. S6 = 103.9
  3. 3. D: Σ (1/2)ᵏ
  4. 4. S = 7.333
  5. 5. S = 0.3679
  6. 6. S = 1.649

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