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

The arithmetic sequence 15, 21, 27, 33, … ends with the term 171. How many terms n does it have?

a₁ = 15d = 6aₙ = 171
n =
2.Easy
kak​123456789101112

The arithmetic sequence 15, 17.5, 20, 22.5, … ends with the term 100. How many terms n does it have?

a₁ = 15d = 2.5aₙ = 100
n =
3.Medium
k|aₖ|¹ᐟᵏ123456789101112

Apply the root test to Σk=1∞ ((3k + 2)/(2k + 1))ᵏ. Find L = lim |ak|1/k.

ak = ((3k + 2)/(2k + 1))ᵏ
L =
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
xyfP₂0.4

Use the Maclaurin polynomial of degree 2 of f(x) = cos(3x) to approximate f(0.4). Give P₂(0.4).

f(x) = cos(3x)n = 2x = 0.4
P₂(0.4) =
6.Hard

Find the coefficient c₂ of (x − 4)² in the Taylor series of f(x) = ln x about a = 4.

f(x) = ln xa = 4k = 2
c₂ =

Answer key

  1. 1. n = 27
  2. 2. n = 35
  3. 3. L = 1.5
  4. 4. L = 0.5
  5. 5. P₂(0.4) = 0.28
  6. 6. c₂ = −0.03125

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