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​12345

Find the sum S5 of the first 5 terms of the geometric sequence 0.5, −1, 2, …

a₁ = 0.5r = −2n = 5
S5 =
2.Easy
kak​123456789101112

Find the sum S35 of the first 35 terms of the arithmetic sequence 16, 13, 10, 7, …

a₁ = 16d = −3n = 35
S35 =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 5ᵏ·xᵏ/(k + 1).

Σ 5ᵏ·xᵏ/(k + 1)x₀ = 0
R =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 12/(k(k + 4)).

ak = 12/(k(k + 4))
S =
5.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 4 at x = 0.3. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e0.3 = 1.35 to find the largest possible error |R₄|.

f(x) = eˣn = 4x = 0.3M = 1.35
|R₄| =
6.Hard

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

ak = (−1)ᵏ·0.52k+1/(2k + 1)!
S =

Answer key

  1. 1. S5 = 5.5
  2. 2. S35 = −1225
  3. 3. R = 0.2
  4. 4. S = 6.25
  5. 5. |R₄| = 2.733 × 10⁻⁵
  6. 6. S = 0.4794

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