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​12345678

Find the sum S8 of the first 8 terms of the geometric sequence 1, 0.8, 0.64, …

a₁ = 1r = 0.8n = 8
S8 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 9·(−2/3)ᵏ.

a = 9r = −2/3k₀ = 1
S =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·8ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·8ᵏ/(2k)!
L =
4.Medium
k|aₖ|¹ᐟᵏ123456789101112

Apply the root test to Σk=1∞ ((4k + 1)/(3k + 4))ᵏ. Find L = lim |ak|1/k.

ak = ((4k + 1)/(3k + 4))ᵏ
L =
5.Hard

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1·0.75ᵏ/k.

ak = (−1)k+1·0.75ᵏ/k
S =
6.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 1 × 10⁻⁵.

f(x) = sin xx = 2M = 1ε = 1 × 10⁻⁵
n =

Answer key

  1. 1. S8 = 4.161
  2. 2. S = −3.6
  3. 3. L = 2
  4. 4. L = 1.333
  5. 5. S = 0.5596
  6. 6. n = 11

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