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​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 0.5, 1, 2, …

a₁ = 0.5r = 2n = 9
S9 =
2.Easy
kak​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 4, 2, 1, …

a₁ = 4r = 0.5n = 7
S7 =
3.Medium
kSn​12345678910

Find the sum S = Σk=131 3/(k(k + 1)).

ak = 3/(k(k + 1))n = 31
S =
4.Medium
k|aₖ|¹ᐟᵏ123456789101112

Apply the root test to Σk=1∞ ((3k + 2)/(5k + 1))ᵏ. Find L = lim |ak|1/k.

ak = ((3k + 2)/(5k + 1))ᵏ
L =
5.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| =
6.Hard
xyfP₅2.5

Use the Maclaurin polynomial of degree 5 of f(x) = sin x to approximate f(2.5). Give P₅(2.5).

f(x) = sin xn = 5x = 2.5
P₅(2.5) =

Answer key

  1. 1. S9 = 255.5
  2. 2. S7 = 7.938
  3. 3. S = 2.906
  4. 4. L = 0.6
  5. 5. |R₂| = 0.1899
  6. 6. P₅(2.5) = 0.7096

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