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​123456789101112

Find the term a21 of the arithmetic sequence 18, 24, 30, 36, …

a₁ = 18d = 6n = 21
a21 =
2.Easy
kak​12345678

Find the sum S8 of the first 8 terms of the geometric sequence 4, −8, 16, …

a₁ = 4r = −2n = 8
S8 =
3.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 =
4.Medium
AΣ (k + 3)/k²k = 1 … ∞BΣ (5/3)ᵏk = 1 … ∞CΣ 1/(k(k + 3))k = 1 … ∞DΣ 2ᵏ/k²k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (k + 3)/k²B: Σ (5/3)ᵏC: Σ 1/(k(k + 3))D: Σ 2ᵏ/k²
  1. 1A: Σ (k + 3)/k²
  2. 2B: Σ (5/3)ᵏ
  3. 3C: Σ 1/(k(k + 3))
  4. 4D: Σ 2ᵏ/k²
5.Hard

Recognise the series and find its sum: S = Σk=0∞ 0.5ᵏ/k!.

ak = 0.5ᵏ/k!
S =
6.Hard

f(x) = cos x is approximated at x = 1.5 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 = 1.5M = 1ε = 0.001
n =

Answer key

  1. 1. a21 = 138
  2. 2. S8 = −340
  3. 3. L = 0.75
  4. 4. C: Σ 1/(k(k + 3))
  5. 5. S = 1.649
  6. 6. n = 7

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