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​123456

Find the sum S6 of the first 6 terms of the geometric sequence 3, 6, 12, …

a₁ = 3r = 2n = 6
S6 =
2.Easy
kak​123456789101112

Find the sum S33 of the first 33 terms of the arithmetic sequence −12, −9, −6, −3, …

a₁ = −12d = 3n = 33
S33 =
3.Medium
k|aₖ|¹ᐟᵏ123456789101112

Apply the root test to Σk=1∞ ((2k + 2)/(6k + 5))ᵏ. Find L = lim |ak|1/k.

ak = ((2k + 2)/(6k + 5))ᵏ
L =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ k·3ᵏ·xᵏ.

Σ k·3ᵏ·xᵏx₀ = 0
R =
5.Hard
xyfP₃0.4

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

f(x) = sin x is approximated at x = 0.5 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 1, find the smallest degree n that guarantees an error below 1 × 10⁻⁶.

f(x) = sin xx = 0.5M = 1ε = 1 × 10⁻⁶
n =

Answer key

  1. 1. S6 = 189
  2. 2. S33 = 1188
  3. 3. L = 0.3333
  4. 4. R = 0.3333
  5. 5. P₃(0.4) = 1.624
  6. 6. n = 7

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