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​1234567891011

The arithmetic sequence 11, 11.5, 12, 12.5, … ends with the term 16. How many terms n does it have?

a₁ = 11d = 0.5aₙ = 16
n =
2.Easy
kak​13579111315ε = 0.2

A ball is dropped and its first rebound reaches 3 m. Every next rebound reaches 90% of the previous one. Which rebound n is the first one lower than 0.2 m?

a₁ = 3r = 0.9ε = 0.2
n =
3.Medium
AΣ (5k + 1)/(k + 2)k = 1 … ∞BΣ (4/5)ᵏk = 1 … ∞CΣ 5/k²k = 1 … ∞DΣ 1/(k² + 1)k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (5k + 1)/(k + 2)B: Σ (4/5)ᵏC: Σ 5/k²D: Σ 1/(k² + 1)
  1. 1A: Σ (5k + 1)/(k + 2)
  2. 2B: Σ (4/5)ᵏ
  3. 3C: Σ 5/k²
  4. 4D: Σ 1/(k² + 1)
4.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = 3ᵏ·k!/kᵏ
L =
5.Hard

Find the coefficient c₂ of (x + 1)² in the Taylor series of f(x) = e3x about a = −1.

f(x) = e3xa = −1k = 2
c₂ =
6.Hard

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1·0.25ᵏ/k.

ak = (−1)k+1·0.25ᵏ/k
S =

Answer key

  1. 1. n = 11
  2. 2. n = 27
  3. 3. A: Σ (5k + 1)/(k + 2)
  4. 4. L = 1.104
  5. 5. c₂ = 0.224
  6. 6. S = 0.2231

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