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​12345678910

The arithmetic sequence −3, −7, −11, −15, … ends with the term −39. How many terms n does it have?

a₁ = −3d = −4aₙ = −39
n =
2.Easy
kak​13579111315ε = 0.01

The geometric sequence aₙ = 5·0.6ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.01.

a₁ = 5r = 0.6ε = 0.01
n =
3.Medium
AΣ 3ᵏ/k²k = 1 … ∞BΣ 1/(3ᵏ + k)k = 1 … ∞CΣ (1 + 1/k)ᵏk = 1 … ∞DΣ 1/√kk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 3ᵏ/k²B: Σ 1/(3ᵏ + k)C: Σ (1 + 1/k)ᵏD: Σ 1/√k
  1. 1A: Σ 3ᵏ/k²
  2. 2B: Σ 1/(3ᵏ + k)
  3. 3C: Σ (1 + 1/k)ᵏ
  4. 4D: Σ 1/√k
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 3/(k(k + 3)).

ak = 3/(k(k + 3))
S =
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 = e0.5 = 1.649 to find the largest possible error |R₅|.

f(x) = eˣn = 5x = 0.5M = 1.649
|R₅| =
6.Hard
xyfP₄0.5

Use the Maclaurin polynomial of degree 4 of f(x) = 1/(1 − x) to approximate f(0.5). Give P₄(0.5).

f(x) = 1/(1 − x)n = 4x = 0.5
P₄(0.5) =

Answer key

  1. 1. n = 10
  2. 2. n = 14
  3. 3. B: Σ 1/(3ᵏ + k)
  4. 4. S = 1.833
  5. 5. |R₅| = 3.578 × 10⁻⁵
  6. 6. P₄(0.5) = 1.938

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