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 = 0.01

A ball is dropped and its first rebound reaches 2 m. Every next rebound reaches 75% of the previous one. Which rebound n is the first one lower than 0.01 m?

a₁ = 2r = 0.75ε = 0.01
n =
2.Easy
kak​123456789101112

Find the term a20 of the arithmetic sequence −7, −10, −13, −16, …

a₁ = −7d = −3n = 20
a20 =
3.Medium
AΣ 1/k³k = 1 … ∞BΣ 3ᵏ/k³k = 1 … ∞CΣ (−1)ᵏ/kk = 1 … ∞DΣ (1/3)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 1/k³B: Σ 3ᵏ/k³C: Σ (−1)ᵏ/kD: Σ (1/3)ᵏ
  1. 1A: Σ 1/k³
  2. 2B: Σ 3ᵏ/k³
  3. 3C: Σ (−1)ᵏ/k
  4. 4D: Σ (1/3)ᵏ
4.Medium
kSn​12345678910

Find the sum S = Σk=15 2/(k(k + 1)).

ak = 2/(k(k + 1))n = 5
S =
5.Hard

Find the coefficient c₂ of (x − 5)² in the Taylor series of f(x) = 1/x about a = 5.

f(x) = 1/xa = 5k = 2
c₂ =
6.Hard

f(x) = ln(1 + x) is approximated by its Maclaurin polynomial of degree 2 at x = 0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 2! = 2 to find the largest possible error |R₂|.

f(x) = ln(1 + x)n = 2x = 0.5M = 2
|R₂| =

Answer key

  1. 1. n = 20
  2. 2. a20 = −64
  3. 3. B: Σ 3ᵏ/k³
  4. 4. S = 1.667
  5. 5. c₂ = 0.008
  6. 6. |R₂| = 0.04167

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