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​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 10, 30, 90, …

a₁ = 10r = 3n = 7
S7 =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the arithmetic sequence 6, 12, 18, 24, …

a₁ = 6d = 6n = 9
S9 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 4/(k(k + 4)).

ak = 4/(k(k + 4))
S =
4.Medium
AΣ (1 + 1/k)ᵏk = 1 … ∞BΣ (−1)ᵏ/kk = 1 … ∞CΣ k³/5ᵏk = 1 … ∞DΣ (2/3)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (1 + 1/k)ᵏB: Σ (−1)ᵏ/kC: Σ k³/5ᵏD: Σ (2/3)ᵏ
  1. 1A: Σ (1 + 1/k)ᵏ
  2. 2B: Σ (−1)ᵏ/k
  3. 3C: Σ k³/5ᵏ
  4. 4D: Σ (2/3)ᵏ
5.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 4 at x = 1. 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 = 1M = 1
|R₄| =
6.Hard

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1·0.25ᵏ/k.

ak = (−1)k+1·0.25ᵏ/k
S =

Answer key

  1. 1. S7 = 10930
  2. 2. S9 = 270
  3. 3. S = 2.083
  4. 4. A: Σ (1 + 1/k)ᵏ
  5. 5. |R₄| = 0.008333
  6. 6. S = 0.2231

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