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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
kak​123456789101112

The arithmetic sequence −1, 4, 9, 14, … ends with the term 164. How many terms n does it have?

a₁ = −1d = 5aₙ = 164
n =
2.Easy
kak​12345

Find the sum S5 of the first 5 terms of the geometric sequence 0.5, 0.75, 1.125, …

a₁ = 0.5r = 1.5n = 5
S5 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k·5ᵏ/3ᵏ. Find L = lim |ak+1/ak|.

ak = k·5ᵏ/3ᵏ
L =
4.Medium
AΣ k/5ᵏk = 1 … ∞BΣ 1/(k(k + 3))k = 1 … ∞CΣ (−1)ᵏ/kk = 1 … ∞DΣ (1 + 1/k)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ k/5ᵏB: Σ 1/(k(k + 3))C: Σ (−1)ᵏ/kD: Σ (1 + 1/k)ᵏ
  1. 1A: Σ k/5ᵏ
  2. 2B: Σ 1/(k(k + 3))
  3. 3C: Σ (−1)ᵏ/k
  4. 4D: Σ (1 + 1/k)ᵏ
5.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·0.52k/(2k)!.

ak = (−1)ᵏ·0.52k/(2k)!
S =
6.Hard

f(x) = cos 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) = cos xn = 3x = 1.5M = 1
|R₃| =

Answer key

  1. 1. n = 34
  2. 2. S5 = 6.594
  3. 3. L = 1.667
  4. 4. D: Σ (1 + 1/k)ᵏ
  5. 5. S = 0.8776
  6. 6. |R₃| = 0.2109

Full step-by-step solutions: practise this topic on examproblems.com.