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​12345

Find the sum S5 of the first 5 terms of the geometric sequence 1, 0.5, 0.25, …

a₁ = 1r = 0.5n = 5
S5 =
2.Easy
kak​123456789101112

The arithmetic sequence 9, 11.5, 14, 16.5, … ends with the term 41.5. How many terms n does it have?

a₁ = 9d = 2.5aₙ = 41.5
n =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = kᵏ/(3ᵏ·k!)
L =
4.Medium
xx₀ = −1??R

Find the radius of convergence R of the power series Σk=1∞ k!·(x + 1)ᵏ/kᵏ.

Σ k!·(x + 1)ᵏ/kᵏx₀ = −1
R =
5.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 3 at x = −0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₃|.

f(x) = eˣn = 3x = −0.5M = 1
|R₃| =
6.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 4 at x = 0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e0.5 = 1.649 to find the largest possible error |R₄|.

f(x) = eˣn = 4x = 0.5M = 1.649
|R₄| =

Answer key

  1. 1. S5 = 1.938
  2. 2. n = 14
  3. 3. L = 0.9061
  4. 4. R = 2.718
  5. 5. |R₃| = 0.002604
  6. 6. |R₄| = 0.0004294

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