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 sum S15 of the first 15 terms of the arithmetic sequence −10, −6, −2, 2, …

a₁ = −10d = 4n = 15
S15 =
2.Easy
kak​13579111315ε = 0.05

A ball is dropped and its first rebound reaches 8 m. Every next rebound reaches 80% of the previous one. Which rebound n is the first one lower than 0.05 m?

a₁ = 8r = 0.8ε = 0.05
n =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·8ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·8ᵏ/(2k)!
L =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 2)).

ak = 1/(k(k + 2))
S =
5.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 4 at x = 0.8. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e0.8 = 2.226 to find the largest possible error |R₄|.

f(x) = eˣn = 4x = 0.8M = 2.226
|R₄| =
6.Hard

Find the coefficient c₂ of (x − 3)² in the Taylor series of f(x) = ln x about a = 3.

f(x) = ln xa = 3k = 2
c₂ =

Answer key

  1. 1. S15 = 270
  2. 2. n = 24
  3. 3. L = 2
  4. 4. S = 0.75
  5. 5. |R₄| = 0.006077
  6. 6. c₂ = −0.05556

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