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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Name: ____________________   Date: ____________

1.Easy
kak​123456789101112

Find the term a33 of the arithmetic sequence 6, 2, −2, −6, …

a₁ = 6d = −4n = 33
a33 =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 4, −12, 36, …

a₁ = 4r = −3n = 9
S9 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 3/(k(k + 2)).

ak = 3/(k(k + 2))
S =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 12/(k(k + 1)).

ak = 12/(k(k + 1))
S =
5.Hard

f(x) = ln(1 + x) is approximated by its Maclaurin polynomial of degree 3 at x = 0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 3! = 6 to find the largest possible error |R₃|.

f(x) = ln(1 + x)n = 3x = 0.5M = 6
|R₃| =
6.Hard

Recognise the series and find its sum: S = Σk=1∞ k·0.5ᵏ.

ak = k·0.5ᵏ
S =

Answer key

  1. 1. a33 = −122
  2. 2. S9 = 19684
  3. 3. S = 2.25
  4. 4. S = 12
  5. 5. |R₃| = 0.01563
  6. 6. S = 2

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