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​13579111315ε = 0.1

A ball is dropped and its first rebound reaches 10 m. Every next rebound reaches 90% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 10r = 0.9ε = 0.1
n =
2.Easy
kak​123456789101112

Find the term a27 of the arithmetic sequence 19, 19.5, 20, 20.5, …

a₁ = 19d = 0.5n = 27
a27 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 4/(k(k + 4)).

ak = 4/(k(k + 4))
S =
4.Medium
AΣ (−1)ᵏ/kk = 1 … ∞BΣ 3ᵏ/k!k = 1 … ∞CΣ 1/√kk = 1 … ∞DΣ (2/5)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (−1)ᵏ/kB: Σ 3ᵏ/k!C: Σ 1/√kD: Σ (2/5)ᵏ
  1. 1A: Σ (−1)ᵏ/k
  2. 2B: Σ 3ᵏ/k!
  3. 3C: Σ 1/√k
  4. 4D: Σ (2/5)ᵏ
5.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·0.52k/(2k)!.

ak = (−1)ᵏ·0.52k/(2k)!
S =
6.Hard

Recognise the series and find its sum: S = Σk=1∞ k·0.5ᵏ.

ak = k·0.5ᵏ
S =

Answer key

  1. 1. n = 45
  2. 2. a27 = 32
  3. 3. S = 2.083
  4. 4. C: Σ 1/√k
  5. 5. S = 0.8776
  6. 6. S = 2

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