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 3, 3.6, 4.32, …

a₁ = 3r = 1.2n = 10
S10 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 12·(−2/3)ᵏ.

a = 12r = −2/3k₀ = 1
S =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·3ᵏ/(2k)!. Find L = lim |ak+1/ak|.

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

Exactly one of the four series converges. Click it.

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

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 4 at x = 0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e0.5 = 1.649 to find the largest possible error |R₄|.

f(x) = eˣn = 4x = 0.5M = 1.649
|R₄| =
6.Hard

Find the coefficient c₂ of (x − 2)² in the Taylor series of f(x) = e3x about a = 2.

f(x) = e3xa = 2k = 2
c₂ =

Answer key

  1. 1. S10 = 77.88
  2. 2. S = −4.8
  3. 3. L = 0.75
  4. 4. A: Σ k/3ᵏ
  5. 5. |R₄| = 0.0004294
  6. 6. c₂ = 1815

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