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​12345678910ε = 0.01

A ball is dropped and its first rebound reaches 2 m. Every next rebound reaches 50% of the previous one. Which rebound n is the first one lower than 0.01 m?

a₁ = 2r = 0.5ε = 0.01
n =
2.Easy
kak​123456789101112

Find the sum S19 of the first 19 terms of the arithmetic sequence 3, 5, 7, 9, …

a₁ = 3d = 2n = 19
S19 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 2)).

ak = 1/(k(k + 2))
S =
4.Medium
AΣ (−1)ᵏ/kk = 1 … ∞BΣ (1 + 1/k)ᵏk = 1 … ∞CΣ 1/(3ᵏ + k)k = 1 … ∞DΣ (2/3)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (−1)ᵏ/kB: Σ (1 + 1/k)ᵏC: Σ 1/(3ᵏ + k)D: Σ (2/3)ᵏ
  1. 1A: Σ (−1)ᵏ/k
  2. 2B: Σ (1 + 1/k)ᵏ
  3. 3C: Σ 1/(3ᵏ + k)
  4. 4D: Σ (2/3)ᵏ
5.Hard
xyfP₂−0.4

Use the Maclaurin polynomial of degree 2 of f(x) = 1/(1 + x) to approximate f(−0.4). Give P₂(−0.4).

f(x) = 1/(1 + x)n = 2x = −0.4
P₂(−0.4) =
6.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 4 at x = 0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₄|.

f(x) = cos xn = 4x = 0.5M = 1
|R₄| =

Answer key

  1. 1. n = 9
  2. 2. S19 = 399
  3. 3. S = 0.75
  4. 4. B: Σ (1 + 1/k)ᵏ
  5. 5. P₂(−0.4) = 1.56
  6. 6. |R₄| = 0.0002604

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