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
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 18·(1/2)ᵏ.

a = 18r = 1/2k₀ = 2
S =
2.Easy
kak​123456789101112

The arithmetic sequence 20, 17, 14, 11, … ends with the term −16. How many terms n does it have?

a₁ = 20d = −3aₙ = −16
n =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 3/(k(k + 2)).

ak = 3/(k(k + 2))
S =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = kᵏ/(3ᵏ·k!)
L =
5.Hard
xyfP₃0.5

Use the Maclaurin polynomial of degree 3 of f(x) = ln(1 − x) to approximate f(0.5). Give P₃(0.5).

f(x) = ln(1 − x)n = 3x = 0.5
P₃(0.5) =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·1.22k/(2k)!.

ak = (−1)ᵏ·1.22k/(2k)!
S =

Answer key

  1. 1. S = 9
  2. 2. n = 13
  3. 3. S = 2.25
  4. 4. L = 0.9061
  5. 5. P₃(0.5) = −0.6667
  6. 6. S = 0.3624

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