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​12345678910

Find the sum S10 of the first 10 terms of the geometric sequence 10, −30, 90, …

a₁ = 10r = −3n = 10
S10 =
2.Easy
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The arithmetic sequence −2, 0.5, 3, 5.5, … ends with the term 68. How many terms n does it have?

a₁ = −2d = 2.5aₙ = 68
n =
3.Medium
AΣ 2/k²k = 1 … ∞BΣ (−1)ᵏ/kk = 1 … ∞CΣ k/5ᵏk = 1 … ∞DΣ ln k / kk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 2/k²B: Σ (−1)ᵏ/kC: Σ k/5ᵏD: Σ ln k / k
  1. 1A: Σ 2/k²
  2. 2B: Σ (−1)ᵏ/k
  3. 3C: Σ k/5ᵏ
  4. 4D: Σ ln k / k
4.Medium
AΣ (4/3)ᵏk = 1 … ∞BΣ 1/√kk = 1 … ∞CΣ (3k + 1)/(k + 2)k = 1 … ∞DΣ 10ᵏ/k!k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (4/3)ᵏB: Σ 1/√kC: Σ (3k + 1)/(k + 2)D: Σ 10ᵏ/k!
  1. 1A: Σ (4/3)ᵏ
  2. 2B: Σ 1/√k
  3. 3C: Σ (3k + 1)/(k + 2)
  4. 4D: Σ 10ᵏ/k!
5.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 3 at x = −0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₃|.

f(x) = cos xn = 3x = −0.5M = 1
|R₃| =
6.Hard
xyfP₄0.5

Use the Maclaurin polynomial of degree 4 of f(x) = cos(3x) to approximate f(0.5). Give P₄(0.5).

f(x) = cos(3x)n = 4x = 0.5
P₄(0.5) =

Answer key

  1. 1. S10 = −147620
  2. 2. n = 29
  3. 3. D: Σ ln k / k
  4. 4. D: Σ 10ᵏ/k!
  5. 5. |R₃| = 0.002604
  6. 6. P₄(0.5) = 0.08594

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