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​12345678

Find the sum S8 of the first 8 terms of the geometric sequence 10, 8, 6.4, …

a₁ = 10r = 0.8n = 8
S8 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 9·(−2/5)ᵏ.

a = 9r = −2/5k₀ = 1
S =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 2/(k(k + 3)).

ak = 2/(k(k + 3))
S =
4.Medium
xx₀ = 2??R

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

Σ k·2ᵏ·(x − 2)ᵏx₀ = 2
x =
5.Hard

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

f(x) = e−xa = 2k = 2
c₂ =
6.Hard

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

ak = (−1)ᵏ·0.52k/(2k)!
S =

Answer key

  1. 1. S8 = 41.61
  2. 2. S = −2.571
  3. 3. S = 1.222
  4. 4. x = 1.5
  5. 5. c₂ = 0.06767
  6. 6. S = 0.8776

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