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 4, −12, 36, …

a₁ = 4r = −3n = 8
S8 =
2.Easy
kak​123456789101112

Find the sum S38 of the first 38 terms of the arithmetic sequence −9, −6.5, −4, −1.5, …

a₁ = −9d = 2.5n = 38
S38 =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 9ᵏx²ᵏ/k.

Σ 9ᵏx²ᵏ/kx₀ = 0
R =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·2ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·2ᵏ/(2k)!
L =
5.Hard

Find the coefficient c₃ of (x − 2)³ in the Taylor series of f(x) = eˣ about a = 2.

f(x) = eˣa = 2k = 3
c₃ =
6.Hard

f(x) = eˣ 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 = 2, find the smallest degree n that guarantees an error below 1 × 10⁻⁶.

f(x) = eˣx = 0.5M = 2ε = 1 × 10⁻⁶
n =

Answer key

  1. 1. S8 = −6560
  2. 2. S38 = 1416
  3. 3. R = 0.3333
  4. 4. L = 0.5
  5. 5. c₃ = 1.232
  6. 6. n = 7

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