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 S32 of the first 32 terms of the arithmetic sequence 17, 18.5, 20, 21.5, …

a₁ = 17d = 1.5n = 32
S32 =
2.Easy
kak​123456789101112

Find the sum S39 of the first 39 terms of the arithmetic sequence 20, 22.5, 25, 27.5, …

a₁ = 20d = 2.5n = 39
S39 =
3.Medium
AΣ 2ᵏ/k²k = 1 … ∞BΣ 1/√kk = 1 … ∞CΣ k/5ᵏk = 1 … ∞DΣ k/(k + 7)k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 2ᵏ/k²B: Σ 1/√kC: Σ k/5ᵏD: Σ k/(k + 7)
  1. 1A: Σ 2ᵏ/k²
  2. 2B: Σ 1/√k
  3. 3C: Σ k/5ᵏ
  4. 4D: Σ k/(k + 7)
4.Medium
AΣ 2/k²k = 1 … ∞BΣ 3ᵏ/k!k = 1 … ∞CΣ (4/3)ᵏk = 1 … ∞DΣ (1/2)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 2/k²B: Σ 3ᵏ/k!C: Σ (4/3)ᵏD: Σ (1/2)ᵏ
  1. 1A: Σ 2/k²
  2. 2B: Σ 3ᵏ/k!
  3. 3C: Σ (4/3)ᵏ
  4. 4D: Σ (1/2)ᵏ
5.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·0.52k+1/(2k + 1)!.

ak = (−1)ᵏ·0.52k+1/(2k + 1)!
S =
6.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 5 at x = 1. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e1 = 2.718 to find the largest possible error |R₅|.

f(x) = eˣn = 5x = 1M = 2.718
|R₅| =

Answer key

  1. 1. S32 = 1288
  2. 2. S39 = 2633
  3. 3. C: Σ k/5ᵏ
  4. 4. C: Σ (4/3)ᵏ
  5. 5. S = 0.4794
  6. 6. |R₅| = 0.003775

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