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​123456789101112

Find the sum S24 of the first 24 terms of the arithmetic sequence 13, 19, 25, 31, …

a₁ = 13d = 6n = 24
S24 =
2.Easy
kak​13579111315ε = 0.1

A ball is dropped and its first rebound reaches 5 m. Every next rebound reaches 80% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 5r = 0.8ε = 0.1
n =
3.Medium
AΣ k/(k + 6)k = 1 … ∞BΣ 1/k⁴k = 1 … ∞CΣ 2ᵏ/k³k = 1 … ∞DΣ 1/(2k + 6)k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ k/(k + 6)B: Σ 1/k⁴C: Σ 2ᵏ/k³D: Σ 1/(2k + 6)
  1. 1A: Σ k/(k + 6)
  2. 2B: Σ 1/k⁴
  3. 3C: Σ 2ᵏ/k³
  4. 4D: Σ 1/(2k + 6)
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

Find the coefficient c₂ of (x − 3)² in the Taylor series of f(x) = ln x about a = 3.

f(x) = ln xa = 3k = 2
c₂ =
6.Hard

Find the coefficient c₂ of (x + 1)² in the Taylor series of f(x) = e−x about a = −1.

f(x) = e−xa = −1k = 2
c₂ =

Answer key

  1. 1. S24 = 1968
  2. 2. n = 19
  3. 3. B: Σ 1/k⁴
  4. 4. L = 0.7358
  5. 5. c₂ = −0.05556
  6. 6. c₂ = 1.359

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