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​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 2, 1.6, 1.28, …

a₁ = 2r = 0.8n = 9
S9 =
2.Easy
kak​12345

Find the sum S5 of the first 5 terms of the geometric sequence 10, −5, 2.5, …

a₁ = 10r = −0.5n = 5
S5 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k³·3ᵏ/5ᵏ. Find L = lim |ak+1/ak|.

ak = k³·3ᵏ/5ᵏ
L =
4.Medium
AΣ (k + 1)/k²k = 1 … ∞BΣ 3ᵏ/k²k = 1 … ∞CΣ 2/kk = 1 … ∞DΣ 1/(k² + 3)k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (k + 1)/k²B: Σ 3ᵏ/k²C: Σ 2/kD: Σ 1/(k² + 3)
  1. 1A: Σ (k + 1)/k²
  2. 2B: Σ 3ᵏ/k²
  3. 3C: Σ 2/k
  4. 4D: Σ 1/(k² + 3)
5.Hard
xyfP₄0.5

Use the Maclaurin polynomial of degree 4 of f(x) = 1/(1 + x) to approximate f(0.5). Give P₄(0.5).

f(x) = 1/(1 + x)n = 4x = 0.5
P₄(0.5) =
6.Hard

f(x) = eˣ 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 = e0.8 = 2.226 to find the largest possible error |R₂|.

f(x) = eˣn = 2x = 0.8M = 2.226
|R₂| =

Answer key

  1. 1. S9 = 8.658
  2. 2. S5 = 6.875
  3. 3. L = 0.6
  4. 4. D: Σ 1/(k² + 3)
  5. 5. P₄(0.5) = 0.6875
  6. 6. |R₂| = 0.1899

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