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​123456789101112

Find the sum S23 of the first 23 terms of the arithmetic sequence −8, −6, −4, −2, …

a₁ = −8d = 2n = 23
S23 =
2.Easy
kak​123456789101112

The arithmetic sequence 10, 7, 4, 1, … ends with the term −77. How many terms n does it have?

a₁ = 10d = −3aₙ = −77
n =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 4ᵏx²ᵏ/k.

Σ 4ᵏx²ᵏ/kx₀ = 0
R =
4.Medium
AΣ (1/3)ᵏk = 1 … ∞BΣ ln k / kk = 1 … ∞CΣ 1/(4k + 3)k = 1 … ∞DΣ k/(k + 5)k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (1/3)ᵏB: Σ ln k / kC: Σ 1/(4k + 3)D: Σ k/(k + 5)
  1. 1A: Σ (1/3)ᵏ
  2. 2B: Σ ln k / k
  3. 3C: Σ 1/(4k + 3)
  4. 4D: Σ k/(k + 5)
5.Hard
xyfP₅2.5

Use the Maclaurin polynomial of degree 5 of f(x) = sin x to approximate f(2.5). Give P₅(2.5).

f(x) = sin xn = 5x = 2.5
P₅(2.5) =
6.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 5 at x = 0.3. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₅|.

f(x) = cos xn = 5x = 0.3M = 1
|R₅| =

Answer key

  1. 1. S23 = 322
  2. 2. n = 30
  3. 3. R = 0.5
  4. 4. A: Σ (1/3)ᵏ
  5. 5. P₅(2.5) = 0.7096
  6. 6. |R₅| = 1.012 × 10⁻⁶

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