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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Name: ____________________   Date: ____________

1.Easy
kak​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 3, 9, 27, …

a₁ = 3r = 3n = 7
S7 =
2.Easy
kak​13579111315ε = 0.05

A ball is dropped and its first rebound reaches 10 m. Every next rebound reaches 85% of the previous one. Which rebound n is the first one lower than 0.05 m?

a₁ = 10r = 0.85ε = 0.05
n =
3.Medium
kSn​12345678910

Find the sum S = Σk=114 6/(k(k + 1)).

ak = 6/(k(k + 1))n = 14
S =
4.Medium
AΣ (4/5)ᵏk = 1 … ∞BΣ (7/4)ᵏk = 1 … ∞CΣ k!/2ᵏk = 1 … ∞DΣ (k + 2)/k²k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (4/5)ᵏB: Σ (7/4)ᵏC: Σ k!/2ᵏD: Σ (k + 2)/k²
  1. 1A: Σ (4/5)ᵏ
  2. 2B: Σ (7/4)ᵏ
  3. 3C: Σ k!/2ᵏ
  4. 4D: Σ (k + 2)/k²
5.Hard

f(x) = eˣ is approximated at x = 2 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 8, find the smallest degree n that guarantees an error below 0.001.

f(x) = eˣx = 2M = 8ε = 0.001
n =
6.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 5 at x = 0.8. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₅|.

f(x) = sin xn = 5x = 0.8M = 1
|R₅| =

Answer key

  1. 1. S7 = 3279
  2. 2. n = 34
  3. 3. S = 5.6
  4. 4. A: Σ (4/5)ᵏ
  5. 5. n = 10
  6. 6. |R₅| = 0.0003641

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