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​12345678

Find the sum S8 of the first 8 terms of the arithmetic sequence 20, 25, 30, 35, …

a₁ = 20d = 5n = 8
S8 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 2·(1/2)ᵏ.

a = 2r = 1/2k₀ = 1
S =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 4)).

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

Find the sum S = Σk=1∞ 3/(k(k + 2)).

ak = 3/(k(k + 2))
S =
5.Hard

f(x) = sin x is approximated at x = 2 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 1, find the smallest degree n that guarantees an error below 0.0001.

f(x) = sin xx = 2M = 1ε = 0.0001
n =
6.Hard

f(x) = cos x is approximated at x = 1 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 1, find the smallest degree n that guarantees an error below 0.001.

f(x) = cos xx = 1M = 1ε = 0.001
n =

Answer key

  1. 1. S8 = 300
  2. 2. S = 2
  3. 3. S = 0.5208
  4. 4. S = 2.25
  5. 5. n = 10
  6. 6. n = 6

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