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​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 0.5, 0.6, 0.72, …

a₁ = 0.5r = 1.2n = 7
S7 =
2.Easy
kak​123456789101112

Find the term a16 of the arithmetic sequence −4, −1, 2, 5, …

a₁ = −4d = 3n = 16
a16 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 2/(k(k + 1)).

ak = 2/(k(k + 1))
S =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 4/(k(k + 3)).

ak = 4/(k(k + 3))
S =
5.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| =
6.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 2 at x = 0.8. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e0.8 = 2.226 to find the largest possible error |R₂|.

f(x) = eˣn = 2x = 0.8M = 2.226
|R₂| =

Answer key

  1. 1. S7 = 6.458
  2. 2. a16 = 41
  3. 3. S = 2
  4. 4. S = 2.444
  5. 5. |R₄| = 0.0002604
  6. 6. |R₂| = 0.1899

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