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
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 4·(2/5)ᵏ.

a = 4r = 2/5k₀ = 1
S =
2.Easy
kak​123456789101112

Find the sum S27 of the first 27 terms of the arithmetic sequence −4, −6, −8, −10, …

a₁ = −4d = −2n = 27
S27 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k²·3ᵏ/4ᵏ. Find L = lim |ak+1/ak|.

ak = k²·3ᵏ/4ᵏ
L =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = 3ᵏ·k!/kᵏ
L =
5.Hard

Recognise the series and find its sum: S = Σk=1∞ k·(1/3)ᵏ.

ak = k·(1/3)ᵏ
S =
6.Hard

f(x) = eˣ is approximated at x = 0.5 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 2, find the smallest degree n that guarantees an error below 1 × 10⁻⁶.

f(x) = eˣx = 0.5M = 2ε = 1 × 10⁻⁶
n =

Answer key

  1. 1. S = 2.667
  2. 2. S27 = −810
  3. 3. L = 0.75
  4. 4. L = 1.104
  5. 5. S = 0.75
  6. 6. n = 7

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