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 S21 of the first 21 terms of the arithmetic sequence −3, 0, 3, 6, …

a₁ = −3d = 3n = 21
S21 =
2.Easy
kak​135791113ε = 0.1

The geometric sequence aₙ = 3·0.75ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.1.

a₁ = 3r = 0.75ε = 0.1
n =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 2/(k(k + 1)).

ak = 2/(k(k + 1))
S =
4.Medium
AΣ (2/5)ᵏk = 1 … ∞BΣ (3k + 1)/(k + 2)k = 1 … ∞CΣ (4/3)ᵏk = 1 … ∞DΣ 1/kk = 1 … ∞

Exactly one of the four series converges. Click it.

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

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 5 at x = −0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₅|.

f(x) = eˣn = 5x = −0.5M = 1
|R₅| =
6.Hard
xyfP₂0.8

Use the Maclaurin polynomial of degree 2 of f(x) = e2x to approximate f(0.8). Give P₂(0.8).

f(x) = e2xn = 2x = 0.8
P₂(0.8) =

Answer key

  1. 1. S21 = 567
  2. 2. n = 13
  3. 3. S = 2
  4. 4. A: Σ (2/5)ᵏ
  5. 5. |R₅| = 2.17 × 10⁻⁵
  6. 6. P₂(0.8) = 3.88

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