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 term a20 of the arithmetic sequence −3, −7, −11, −15, …

a₁ = −3d = −4n = 20
a20 =
2.Easy
kak​12345

Find the sum S5 of the first 5 terms of the geometric sequence 10, 8, 6.4, …

a₁ = 10r = 0.8n = 5
S5 =
3.Medium
xx₀ = 3??R

Find the radius of convergence R of the power series Σk=1∞ 2ᵏ·(x − 3)ᵏ/(k + 1).

Σ 2ᵏ·(x − 3)ᵏ/(k + 1)x₀ = 3
R =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k·3ᵏ/4ᵏ. Find L = lim |ak+1/ak|.

ak = k·3ᵏ/4ᵏ
L =
5.Hard
xyfP₃0.5

Use the Maclaurin polynomial of degree 3 of f(x) = ln(1 + x) to approximate f(0.5). Give P₃(0.5).

f(x) = ln(1 + x)n = 3x = 0.5
P₃(0.5) =
6.Hard

Find the coefficient c₂ of (x − 9)² in the Taylor series of f(x) = √x about a = 9.

f(x) = √xa = 9k = 2
c₂ =

Answer key

  1. 1. a20 = −79
  2. 2. S5 = 33.62
  3. 3. R = 0.5
  4. 4. L = 0.75
  5. 5. P₃(0.5) = 0.4167
  6. 6. c₂ = −0.00463

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