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​13579111315ε = 0.1

The geometric sequence aₙ = 3·0.8ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.1.

a₁ = 3r = 0.8ε = 0.1
n =
2.Easy
kak​123456

Find the sum S6 of the first 6 terms of the geometric sequence 1, 2, 4, …

a₁ = 1r = 2n = 6
S6 =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ k²·4ᵏ·xᵏ.

Σ k²·4ᵏ·xᵏx₀ = 0
R =
4.Medium
xx₀ = 2??R

The power series Σk=1∞ k²·5ᵏ·(x − 2)ᵏ converges on an interval around x₀ = 2. Find the right end x of that interval.

Σ k²·5ᵏ·(x − 2)ᵏx₀ = 2
x =
5.Hard
xyfP₅1.2

Use the Maclaurin polynomial of degree 5 of f(x) = sin(2x) to approximate f(1.2). Give P₅(1.2).

f(x) = sin(2x)n = 5x = 1.2
P₅(1.2) =
6.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 4 at x = 0.8. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e0.8 = 2.226 to find the largest possible error |R₄|.

f(x) = eˣn = 4x = 0.8M = 2.226
|R₄| =

Answer key

  1. 1. n = 17
  2. 2. S6 = 63
  3. 3. R = 0.25
  4. 4. x = 2.2
  5. 5. P₅(1.2) = 0.7596
  6. 6. |R₄| = 0.006077

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