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

Find the sum S18 of the first 18 terms of the arithmetic sequence −10, −12, −14, −16, …

a₁ = −10d = −2n = 18
S18 =
2.Easy
kak​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 0.5, 1, 2, …

a₁ = 0.5r = 2n = 7
S7 =
3.Medium
AΣ ln k / kk = 1 … ∞BΣ k³/5ᵏk = 1 … ∞CΣ 3ᵏ/k²k = 1 … ∞DΣ k/(k + 1)k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ ln k / kB: Σ k³/5ᵏC: Σ 3ᵏ/k²D: Σ k/(k + 1)
  1. 1A: Σ ln k / k
  2. 2B: Σ k³/5ᵏ
  3. 3C: Σ 3ᵏ/k²
  4. 4D: Σ k/(k + 1)
4.Medium
k|aₖ|¹ᐟᵏ123456789101112

Apply the root test to Σk=1∞ ((4k + 5)/(5k + 3))ᵏ. Find L = lim |ak|1/k.

ak = ((4k + 5)/(5k + 3))ᵏ
L =
5.Hard

f(x) = ln(1 + x) is approximated by its Maclaurin polynomial of degree 4 at x = 0.3. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 4! = 24 to find the largest possible error |R₄|.

f(x) = ln(1 + x)n = 4x = 0.3M = 24
|R₄| =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·0.82k+1/(2k + 1)!.

ak = (−1)ᵏ·0.82k+1/(2k + 1)!
S =

Answer key

  1. 1. S18 = −486
  2. 2. S7 = 63.5
  3. 3. B: Σ k³/5ᵏ
  4. 4. L = 0.8
  5. 5. |R₄| = 0.000486
  6. 6. S = 0.7174

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