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​1234567891011ε = 0.1

The geometric sequence aₙ = 2·0.7ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.1.

a₁ = 2r = 0.7ε = 0.1
n =
2.Easy
kak​13579111315ε = 0.01

The geometric sequence aₙ = 8·0.8ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.01.

a₁ = 8r = 0.8ε = 0.01
n =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·1ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·1ᵏ/(2k)!
L =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 5/(k(k + 3)).

ak = 5/(k(k + 3))
S =
5.Hard
xyfP₃−0.2

Use the Maclaurin polynomial of degree 3 of f(x) = 1/(1 − 2x) to approximate f(−0.2). Give P₃(−0.2).

f(x) = 1/(1 − 2x)n = 3x = −0.2
P₃(−0.2) =
6.Hard

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1·0.2ᵏ/k.

ak = (−1)k+1·0.2ᵏ/k
S =

Answer key

  1. 1. n = 10
  2. 2. n = 31
  3. 3. L = 0.25
  4. 4. S = 3.056
  5. 5. P₃(−0.2) = 0.696
  6. 6. S = 0.1823

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