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 S38 of the first 38 terms of the arithmetic sequence −6, −1, 4, 9, …

a₁ = −6d = 5n = 38
S38 =
2.Easy
kak​13579111315ε = 0.01

A ball is dropped and its first rebound reaches 2 m. Every next rebound reaches 80% of the previous one. Which rebound n is the first one lower than 0.01 m?

a₁ = 2r = 0.8ε = 0.01
n =
3.Medium
AΣ (5/4)ᵏk = 1 … ∞BΣ (3k + 1)/(k + 2)k = 1 … ∞CΣ k!/3ᵏk = 1 … ∞DΣ 1/k³k = 1 … ∞

Exactly one of the four series converges. Click it.

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

The power series Σk=1∞ k!·(x + 2)ᵏ/kᵏ converges on an interval around x₀ = −2. Find the right end x of that interval.

Σ k!·(x + 2)ᵏ/kᵏx₀ = −2
x =
5.Hard

Find the coefficient c₂ of (x − 4)² in the Taylor series of f(x) = √x about a = 4.

f(x) = √xa = 4k = 2
c₂ =
6.Hard

f(x) = ln(1 + x) is approximated by its Maclaurin polynomial of degree 3 at x = 0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 3! = 6 to find the largest possible error |R₃|.

f(x) = ln(1 + x)n = 3x = 0.5M = 6
|R₃| =

Answer key

  1. 1. S38 = 3287
  2. 2. n = 25
  3. 3. D: Σ 1/k³
  4. 4. x = 0.7183
  5. 5. c₂ = −0.01563
  6. 6. |R₃| = 0.01563

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