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​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 3, 6, 12, …

a₁ = 3r = 2n = 9
S9 =
2.Easy
kak​123456789101112

Find the sum S14 of the first 14 terms of the arithmetic sequence 6, 12, 18, 24, …

a₁ = 6d = 6n = 14
S14 =
3.Medium
AΣ 3ᵏ/k³k = 1 … ∞BΣ 1/(2ᵏ + k)k = 1 … ∞CΣ k/(k + 1)k = 1 … ∞DΣ 5/kk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 3ᵏ/k³B: Σ 1/(2ᵏ + k)C: Σ k/(k + 1)D: Σ 5/k
  1. 1A: Σ 3ᵏ/k³
  2. 2B: Σ 1/(2ᵏ + k)
  3. 3C: Σ k/(k + 1)
  4. 4D: Σ 5/k
4.Medium
xx₀ = −1??R

Find the radius of convergence R of the power series Σk=1∞ k!·(x + 1)ᵏ/kᵏ.

Σ k!·(x + 1)ᵏ/kᵏx₀ = −1
R =
5.Hard

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

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

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·22k+1/(2k + 1)!.

ak = (−1)ᵏ·22k+1/(2k + 1)!
S =

Answer key

  1. 1. S9 = 1533
  2. 2. S14 = 630
  3. 3. B: Σ 1/(2ᵏ + k)
  4. 4. R = 2.718
  5. 5. |R₅| = 0.001389
  6. 6. S = 0.9093

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