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​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 3, −1.5, 0.75, …

a₁ = 3r = −0.5n = 7
S7 =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the arithmetic sequence 10, 15, 20, 25, …

a₁ = 10d = 5n = 9
S9 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = kᵏ/(2ᵏ·k!)
L =
4.Medium
AΣ k!/2ᵏk = 1 … ∞BΣ (1/2)ᵏk = 1 … ∞CΣ 3/k²k = 1 … ∞DΣ 1/(k(k + 2))k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ k!/2ᵏB: Σ (1/2)ᵏC: Σ 3/k²D: Σ 1/(k(k + 2))
  1. 1A: Σ k!/2ᵏ
  2. 2B: Σ (1/2)ᵏ
  3. 3C: Σ 3/k²
  4. 4D: Σ 1/(k(k + 2))
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 1 × 10⁻⁶.

f(x) = eˣx = 2M = 8ε = 1 × 10⁻⁶
n =
6.Hard

f(x) = cos x 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 = 1, find the smallest degree n that guarantees an error below 1 × 10⁻⁵.

f(x) = cos xx = 0.5M = 1ε = 1 × 10⁻⁵
n =

Answer key

  1. 1. S7 = 2.016
  2. 2. S9 = 270
  3. 3. L = 1.359
  4. 4. A: Σ k!/2ᵏ
  5. 5. n = 14
  6. 6. n = 6

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