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 term a17 of the arithmetic sequence −5, −8, −11, −14, …

a₁ = −5d = −3n = 17
a17 =
2.Easy
kak​12345

Find the sum S5 of the first 5 terms of the geometric sequence 4, 4.8, 5.76, …

a₁ = 4r = 1.2n = 5
S5 =
3.Medium
AΣ 2/k⁴k = 1 … ∞BΣ ln k / kk = 1 … ∞CΣ (4/5)ᵏk = 1 … ∞DΣ 1/(2ᵏ + k)k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 2/k⁴B: Σ ln k / kC: Σ (4/5)ᵏD: Σ 1/(2ᵏ + k)
  1. 1A: Σ 2/k⁴
  2. 2B: Σ ln k / k
  3. 3C: Σ (4/5)ᵏ
  4. 4D: Σ 1/(2ᵏ + k)
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 2/(k(k + 4)).

ak = 2/(k(k + 4))
S =
5.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 4 at x = 1.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₄|.

f(x) = sin xn = 4x = 1.5M = 1
|R₄| =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·1.22k/(2k)!.

ak = (−1)ᵏ·1.22k/(2k)!
S =

Answer key

  1. 1. a17 = −53
  2. 2. S5 = 29.77
  3. 3. B: Σ ln k / k
  4. 4. S = 1.042
  5. 5. |R₄| = 0.06328
  6. 6. S = 0.3624

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