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​123456789101112

Find the sum S36 of the first 36 terms of the arithmetic sequence 17, 22, 27, 32, …

a₁ = 17d = 5n = 36
S36 =
2.Easy
kak​1234567ε = 0.1

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 0.1 m?

a₁ = 2r = 0.5ε = 0.1
n =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = kᵏ/(5ᵏ·k!)
L =
4.Medium
AΣ ln k / kk = 1 … ∞BΣ (5/3)ᵏk = 1 … ∞CΣ k/5ᵏk = 1 … ∞DΣ k!/2ᵏk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ ln k / kB: Σ (5/3)ᵏC: Σ k/5ᵏD: Σ k!/2ᵏ
  1. 1A: Σ ln k / k
  2. 2B: Σ (5/3)ᵏ
  3. 3C: Σ k/5ᵏ
  4. 4D: Σ k!/2ᵏ
5.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 5 at x = 0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₅|.

f(x) = cos xn = 5x = 0.5M = 1
|R₅| =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ 2ᵏ/k!.

ak = 2ᵏ/k!
S =

Answer key

  1. 1. S36 = 3762
  2. 2. n = 6
  3. 3. L = 0.5437
  4. 4. C: Σ k/5ᵏ
  5. 5. |R₅| = 2.17 × 10⁻⁵
  6. 6. S = 7.389

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