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

The arithmetic sequence 6, 4, 2, 0, … ends with the term −34. How many terms n does it have?

a₁ = 6d = −2aₙ = −34
n =
2.Easy
kak​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 4, 3.2, 2.56, …

a₁ = 4r = 0.8n = 7
S7 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 3)).

ak = 1/(k(k + 3))
S =
4.Medium
AΣ (5/3)ᵏk = 1 … ∞BΣ (−1)ᵏ/√kk = 1 … ∞CΣ k/(k + 1)k = 1 … ∞DΣ (k + 3)/k²k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (5/3)ᵏB: Σ (−1)ᵏ/√kC: Σ k/(k + 1)D: Σ (k + 3)/k²
  1. 1A: Σ (5/3)ᵏ
  2. 2B: Σ (−1)ᵏ/√k
  3. 3C: Σ k/(k + 1)
  4. 4D: Σ (k + 3)/k²
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
xyfP₂1.5

Use the Maclaurin polynomial of degree 2 of f(x) = e0.5x to approximate f(1.5). Give P₂(1.5).

f(x) = e0.5xn = 2x = 1.5
P₂(1.5) =

Answer key

  1. 1. n = 21
  2. 2. S7 = 15.81
  3. 3. S = 0.6111
  4. 4. B: Σ (−1)ᵏ/√k
  5. 5. |R₄| = 0.06328
  6. 6. P₂(1.5) = 2.031

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