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​12345678

Find the sum S8 of the first 8 terms of the geometric sequence 0.5, 1, 2, …

a₁ = 0.5r = 2n = 8
S8 =
2.Easy
kak​123456789101112

Find the term a28 of the arithmetic sequence 4, 9, 14, 19, …

a₁ = 4d = 5n = 28
a28 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 2/(k(k + 2)).

ak = 2/(k(k + 2))
S =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 4ᵏx²ᵏ/k.

Σ 4ᵏx²ᵏ/kx₀ = 0
R =
5.Hard
xyfP₃−0.5

Use the Maclaurin polynomial of degree 3 of f(x) = sin(3x) to approximate f(−0.5). Give P₃(−0.5).

f(x) = sin(3x)n = 3x = −0.5
P₃(−0.5) =
6.Hard

f(x) = eˣ is approximated at x = 2 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 8, find the smallest degree n that guarantees an error below 1 × 10⁻⁵.

f(x) = eˣx = 2M = 8ε = 1 × 10⁻⁵
n =

Answer key

  1. 1. S8 = 127.5
  2. 2. a28 = 139
  3. 3. S = 1.5
  4. 4. R = 0.5
  5. 5. P₃(−0.5) = −0.9375
  6. 6. n = 13

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