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​13579111315ε = 0.1

A ball is dropped and its first rebound reaches 10 m. Every next rebound reaches 80% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 10r = 0.8ε = 0.1
n =
2.Easy
kak​123456789101112

Find the sum S30 of the first 30 terms of the arithmetic sequence 2, 7, 12, 17, …

a₁ = 2d = 5n = 30
S30 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 6/(k(k + 3)).

ak = 6/(k(k + 3))
S =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 12/(k(k + 4)).

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

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

ak = (−1)ᵏ/(2k)!
S =
6.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 5 at x = 1.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₅|.

f(x) = sin xn = 5x = 1.5M = 1
|R₅| =

Answer key

  1. 1. n = 22
  2. 2. S30 = 2235
  3. 3. S = 3.667
  4. 4. S = 6.25
  5. 5. S = 0.5403
  6. 6. |R₅| = 0.01582

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