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 3, 3.6, 4.32, …

a₁ = 3r = 1.2n = 9
S9 =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 2, −4, 8, …

a₁ = 2r = −2n = 9
S9 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 3/(k(k + 3)).

ak = 3/(k(k + 3))
S =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = (k!)²·3ᵏ/(2k)!
L =
5.Hard

f(x) = eˣ is approximated at x = 2 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 8, find the smallest degree n that guarantees an error below 0.0005.

f(x) = eˣx = 2M = 8ε = 0.0005
n =
6.Hard

Find the coefficient c₃ of (x + 1)³ in the Taylor series of f(x) = e2x about a = −1.

f(x) = e2xa = −1k = 3
c₃ =

Answer key

  1. 1. S9 = 62.4
  2. 2. S9 = 342
  3. 3. S = 1.833
  4. 4. L = 0.75
  5. 5. n = 10
  6. 6. c₃ = 0.1804

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