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​12345678

Find the sum S8 of the first 8 terms of the geometric sequence 10, 30, 90, …

a₁ = 10r = 3n = 8
S8 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 5·(−2/5)ᵏ.

a = 5r = −2/5k₀ = 2
S =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 3/(k(k + 4)).

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

Find the sum S = Σk=114 1/(k(k + 1)).

ak = 1/(k(k + 1))n = 14
S =
5.Hard

Recognise the series and find its sum: S = Σk=0∞ 0.5ᵏ/k!.

ak = 0.5ᵏ/k!
S =
6.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 4 at x = 0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₄|.

f(x) = cos xn = 4x = 0.5M = 1
|R₄| =

Answer key

  1. 1. S8 = 32800
  2. 2. S = 0.5714
  3. 3. S = 1.562
  4. 4. S = 0.9333
  5. 5. S = 1.649
  6. 6. |R₄| = 0.0002604

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