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 term a29 of the arithmetic sequence 16, 22, 28, 34, …

a₁ = 16d = 6n = 29
a29 =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 5, 4, 3.2, …

a₁ = 5r = 0.8n = 9
S9 =
3.Medium
AΣ k/5ᵏk = 1 … ∞BΣ 1/√kk = 1 … ∞CΣ 1/k²k = 1 … ∞DΣ 1/(k(k + 3))k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ k/5ᵏB: Σ 1/√kC: Σ 1/k²D: Σ 1/(k(k + 3))
  1. 1A: Σ k/5ᵏ
  2. 2B: Σ 1/√k
  3. 3C: Σ 1/k²
  4. 4D: Σ 1/(k(k + 3))
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ k²·3ᵏ·xᵏ.

Σ k²·3ᵏ·xᵏx₀ = 0
R =
5.Hard

Recognise the series and find its sum: S = Σk=1∞ k·0.5ᵏ.

ak = k·0.5ᵏ
S =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·22k+1/(2k + 1)!.

ak = (−1)ᵏ·22k+1/(2k + 1)!
S =

Answer key

  1. 1. a29 = 184
  2. 2. S9 = 21.64
  3. 3. B: Σ 1/√k
  4. 4. R = 0.3333
  5. 5. S = 2
  6. 6. S = 0.9093

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