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

The arithmetic sequence 15, 18, 21, 24, … ends with the term 120. How many terms n does it have?

a₁ = 15d = 3aₙ = 120
n =
2.Easy
kak​123456789101112

Find the sum S38 of the first 38 terms of the arithmetic sequence 17, 15, 13, 11, …

a₁ = 17d = −2n = 38
S38 =
3.Medium
AΣ (3/2)ᵏk = 1 … ∞BΣ (−1)ᵏ/kk = 1 … ∞CΣ k!/10ᵏk = 1 … ∞DΣ ln k / kk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (3/2)ᵏB: Σ (−1)ᵏ/kC: Σ k!/10ᵏD: Σ ln k / k
  1. 1A: Σ (3/2)ᵏ
  2. 2B: Σ (−1)ᵏ/k
  3. 3C: Σ k!/10ᵏ
  4. 4D: Σ ln k / k
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·3ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·3ᵏ/(2k)!
L =
5.Hard

f(x) = eˣ is approximated at x = 0.5 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 2, find the smallest degree n that guarantees an error below 0.0005.

f(x) = eˣx = 0.5M = 2ε = 0.0005
n =
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 = 36
  2. 2. S38 = −760
  3. 3. B: Σ (−1)ᵏ/k
  4. 4. L = 0.75
  5. 5. n = 5
  6. 6. P₄(0.5) = 1.938

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