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

Find the sum S17 of the first 17 terms of the arithmetic sequence −12, −7, −2, 3, …

a₁ = −12d = 5n = 17
S17 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 8·(−1/3)ᵏ.

a = 8r = −1/3k₀ = 1
S =
3.Medium
AΣ k²/5ᵏk = 1 … ∞BΣ 1/(k² + 5)k = 1 … ∞CΣ 5/kk = 1 … ∞DΣ (−1)ᵏ/√kk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ k²/5ᵏB: Σ 1/(k² + 5)C: Σ 5/kD: Σ (−1)ᵏ/√k
  1. 1A: Σ k²/5ᵏ
  2. 2B: Σ 1/(k² + 5)
  3. 3C: Σ 5/k
  4. 4D: Σ (−1)ᵏ/√k
4.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = 2ᵏ·k!/kᵏ
L =
5.Hard

f(x) = eˣ 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 = 2, find the smallest degree n that guarantees an error below 1 × 10⁻⁵.

f(x) = eˣx = 0.5M = 2ε = 1 × 10⁻⁵
n =
6.Hard

Find the coefficient c₄ of (x − 1)⁴ in the Taylor series of f(x) = ln x about a = 1.

f(x) = ln xa = 1k = 4
c₄ =

Answer key

  1. 1. S17 = 476
  2. 2. S = −2
  3. 3. C: Σ 5/k
  4. 4. L = 0.7358
  5. 5. n = 6
  6. 6. c₄ = −0.25

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