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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Name: ____________________   Date: ____________

1.Easy
kak​12345678910

Find the term a10 of the arithmetic sequence 18, 22, 26, 30, …

a₁ = 18d = 4n = 10
a10 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 18·(−1/2)ᵏ.

a = 18r = −1/2k₀ = 1
S =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 4/(k(k + 1)).

ak = 4/(k(k + 1))
S =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 4/(k(k + 4)).

ak = 4/(k(k + 4))
S =
5.Hard

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

f(x) = ln xa = 3k = 3
c₃ =
6.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 3 at x = 1.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₃|.

f(x) = sin xn = 3x = 1.5M = 1
|R₃| =

Answer key

  1. 1. a10 = 54
  2. 2. S = −6
  3. 3. S = 4
  4. 4. S = 2.083
  5. 5. c₃ = 0.01235
  6. 6. |R₃| = 0.2109

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