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​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 4, −12, 36, …

a₁ = 4r = −3n = 7
S7 =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 1, 2, 4, …

a₁ = 1r = 2n = 9
S9 =
3.Medium
AΣ (−1)ᵏ/kk = 1 … ∞BΣ k²/3ᵏk = 1 … ∞CΣ 1/(k(k + 3))k = 1 … ∞DΣ (4k + 1)/(k + 2)k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (−1)ᵏ/kB: Σ k²/3ᵏC: Σ 1/(k(k + 3))D: Σ (4k + 1)/(k + 2)
  1. 1A: Σ (−1)ᵏ/k
  2. 2B: Σ k²/3ᵏ
  3. 3C: Σ 1/(k(k + 3))
  4. 4D: Σ (4k + 1)/(k + 2)
4.Medium
AΣ 1/(3k + 5)k = 1 … ∞BΣ (3k + 1)/(k + 2)k = 1 … ∞CΣ (k + 2)/k²k = 1 … ∞DΣ k²/2ᵏk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 1/(3k + 5)B: Σ (3k + 1)/(k + 2)C: Σ (k + 2)/k²D: Σ k²/2ᵏ
  1. 1A: Σ 1/(3k + 5)
  2. 2B: Σ (3k + 1)/(k + 2)
  3. 3C: Σ (k + 2)/k²
  4. 4D: Σ k²/2ᵏ
5.Hard

Find the coefficient c₂ of (x − 1)² in the Taylor series of f(x) = e2x about a = 1.

f(x) = e2xa = 1k = 2
c₂ =
6.Hard

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

ak = (−1)ᵏ/(2k)!
S =

Answer key

  1. 1. S7 = 2188
  2. 2. S9 = 511
  3. 3. D: Σ (4k + 1)/(k + 2)
  4. 4. D: Σ k²/2ᵏ
  5. 5. c₂ = 14.78
  6. 6. S = 0.5403

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