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​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 10, −5, 2.5, …

a₁ = 10r = −0.5n = 9
S9 =
2.Easy
kak​13579111315ε = 0.1

A ball is dropped and its first rebound reaches 10 m. Every next rebound reaches 90% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 10r = 0.9ε = 0.1
n =
3.Medium
AΣ 1/(k² + 8)k = 1 … ∞BΣ (−1)ᵏ/kk = 1 … ∞CΣ 5ᵏ/k!k = 1 … ∞DΣ (5/3)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 1/(k² + 8)B: Σ (−1)ᵏ/kC: Σ 5ᵏ/k!D: Σ (5/3)ᵏ
  1. 1A: Σ 1/(k² + 8)
  2. 2B: Σ (−1)ᵏ/k
  3. 3C: Σ 5ᵏ/k!
  4. 4D: Σ (5/3)ᵏ
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k·5ᵏ/3ᵏ. Find L = lim |ak+1/ak|.

ak = k·5ᵏ/3ᵏ
L =
5.Hard

Find the coefficient c₃ of (x − 4)³ in the Taylor series of f(x) = ln x about a = 4.

f(x) = ln xa = 4k = 3
c₃ =
6.Hard
xyfP₃0.8

Use the Maclaurin polynomial of degree 3 of f(x) = sin(2x) to approximate f(0.8). Give P₃(0.8).

f(x) = sin(2x)n = 3x = 0.8
P₃(0.8) =

Answer key

  1. 1. S9 = 6.68
  2. 2. n = 45
  3. 3. D: Σ (5/3)ᵏ
  4. 4. L = 1.667
  5. 5. c₃ = 0.005208
  6. 6. P₃(0.8) = 0.9173

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