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​1234567891011

Find the sum S11 of the first 11 terms of the arithmetic sequence −12, −10, −8, −6, …

a₁ = −12d = 2n = 11
S11 =
2.Easy
kak​123456789101112

Find the sum S12 of the first 12 terms of the arithmetic sequence 8, 10, 12, 14, …

a₁ = 8d = 2n = 12
S12 =
3.Medium
AΣ (5/4)ᵏk = 1 … ∞BΣ 1/(k² + 4)k = 1 … ∞CΣ k³/5ᵏk = 1 … ∞DΣ (−1)ᵏ/kk = 1 … ∞

Exactly one of the four series diverges. Click it.

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

Find the radius of convergence R of the power series Σk=1∞ (x − 3)ᵏ/(k²·3ᵏ).

Σ (x − 3)ᵏ/(k²·3ᵏ)x₀ = 3
R =
5.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 2 at x = 1.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e1.5 = 4.482 to find the largest possible error |R₂|.

f(x) = eˣn = 2x = 1.5M = 4.482
|R₂| =
6.Hard

f(x) = cos x is approximated at x = 2 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 0.001.

f(x) = cos xx = 2M = 1ε = 0.001
n =

Answer key

  1. 1. S11 = −22
  2. 2. S12 = 228
  3. 3. A: Σ (5/4)ᵏ
  4. 4. R = 3
  5. 5. |R₂| = 2.521
  6. 6. n = 9

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