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

The arithmetic sequence −11, −6, −1, 4, … ends with the term 144. How many terms n does it have?

a₁ = −11d = 5aₙ = 144
n =
2.Easy
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Find the sum S10 of the first 10 terms of the geometric sequence 0.5, 1.5, 4.5, …

a₁ = 0.5r = 3n = 10
S10 =
3.Medium
AΣ k/(k + 2)k = 1 … ∞BΣ (3/5)ᵏk = 1 … ∞CΣ 1/k³k = 1 … ∞DΣ 1/(k² + 2)k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ k/(k + 2)B: Σ (3/5)ᵏC: Σ 1/k³D: Σ 1/(k² + 2)
  1. 1A: Σ k/(k + 2)
  2. 2B: Σ (3/5)ᵏ
  3. 3C: Σ 1/k³
  4. 4D: Σ 1/(k² + 2)
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ k!·xᵏ/kᵏ.

Σ k!·xᵏ/kᵏx₀ = 0
R =
5.Hard

f(x) = sin x is approximated at x = 0.5 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 1, find the smallest degree n that guarantees an error below 1 × 10⁻⁵.

f(x) = sin xx = 0.5M = 1ε = 1 × 10⁻⁵
n =
6.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 2 at x = 0.8. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₂|.

f(x) = sin xn = 2x = 0.8M = 1
|R₂| =

Answer key

  1. 1. n = 32
  2. 2. S10 = 14762
  3. 3. A: Σ k/(k + 2)
  4. 4. R = 2.718
  5. 5. n = 6
  6. 6. |R₂| = 0.08533

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