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​12345

Find the sum S5 of the first 5 terms of the geometric sequence 5, −2.5, 1.25, …

a₁ = 5r = −0.5n = 5
S5 =
2.Easy
kak​12345

Find the sum S5 of the first 5 terms of the geometric sequence 5, −10, 20, …

a₁ = 5r = −2n = 5
S5 =
3.Medium
AΣ (k + 3)/k²k = 1 … ∞BΣ (4/3)ᵏk = 1 … ∞CΣ 2/k²k = 1 … ∞DΣ 2ᵏ/k²k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (k + 3)/k²B: Σ (4/3)ᵏC: Σ 2/k²D: Σ 2ᵏ/k²
  1. 1A: Σ (k + 3)/k²
  2. 2B: Σ (4/3)ᵏ
  3. 3C: Σ 2/k²
  4. 4D: Σ 2ᵏ/k²
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ kᵏ/(5ᵏ·k!). Find L = lim |ak+1/ak|.

ak = kᵏ/(5ᵏ·k!)
L =
5.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 3 at x = 0.3. 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 = 0.3M = 1
|R₃| =
6.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 4 at x = 0.2. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₄|.

f(x) = cos xn = 4x = 0.2M = 1
|R₄| =

Answer key

  1. 1. S5 = 3.438
  2. 2. S5 = 55
  3. 3. C: Σ 2/k²
  4. 4. L = 0.5437
  5. 5. |R₃| = 0.0003375
  6. 6. |R₄| = 2.667 × 10⁻⁶

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