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​12345

Find the sum S5 of the first 5 terms of the geometric sequence 3, 4.5, 6.75, …

a₁ = 3r = 1.5n = 5
S5 =
2.Easy
kak​123456789101112

The arithmetic sequence 1, −1, −3, −5, … ends with the term −57. How many terms n does it have?

a₁ = 1d = −2aₙ = −57
n =
3.Medium
kSn​12345678910

Find the sum S = Σk=16 3/(k(k + 1)).

ak = 3/(k(k + 1))n = 6
S =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ xᵏ/(k·4ᵏ).

Σ xᵏ/(k·4ᵏ)x₀ = 0
R =
5.Hard
xyfP₃−0.4

Use the Maclaurin polynomial of degree 3 of f(x) = 1/(1 + x) to approximate f(−0.4). Give P₃(−0.4).

f(x) = 1/(1 + x)n = 3x = −0.4
P₃(−0.4) =
6.Hard

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

f(x) = ∛xa = 1k = 2
c₂ =

Answer key

  1. 1. S5 = 39.56
  2. 2. n = 30
  3. 3. S = 2.571
  4. 4. R = 4
  5. 5. P₃(−0.4) = 1.624
  6. 6. c₂ = −0.1111

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