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∞ 9·(2/5)ᵏ.

a = 9r = 2/5k₀ = 2
S =
2.Easy
kak​12345678

Find the sum S8 of the first 8 terms of the geometric sequence 10, −5, 2.5, …

a₁ = 10r = −0.5n = 8
S8 =
3.Medium
kSn​12345678910

Find the sum S = Σk=137 4/(k(k + 1)).

ak = 4/(k(k + 1))n = 37
S =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 4ᵏx²ᵏ/k.

Σ 4ᵏx²ᵏ/kx₀ = 0
R =
5.Hard
xyfP₃0.5

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

f(x) = sin(3x)n = 3x = 0.5
P₃(0.5) =
6.Hard

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

ak = (−1)ᵏ/(2k)!
S =

Answer key

  1. 1. S = 2.4
  2. 2. S8 = 6.641
  3. 3. S = 3.895
  4. 4. R = 0.5
  5. 5. P₃(0.5) = 0.9375
  6. 6. S = 0.5403

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