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 S25 of the first 25 terms of the arithmetic sequence 11, 17, 23, 29, …

a₁ = 11d = 6n = 25
S25 =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 4, −2, 1, …

a₁ = 4r = −0.5n = 9
S9 =
3.Medium
AΣ 1/√kk = 1 … ∞BΣ (4/3)ᵏk = 1 … ∞CΣ (−1)ᵏ/√kk = 1 … ∞DΣ k!/10ᵏk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 1/√kB: Σ (4/3)ᵏC: Σ (−1)ᵏ/√kD: Σ k!/10ᵏ
  1. 1A: Σ 1/√k
  2. 2B: Σ (4/3)ᵏ
  3. 3C: Σ (−1)ᵏ/√k
  4. 4D: Σ k!/10ᵏ
4.Medium
xx₀ = 3??R

Find the radius of convergence R of the power series Σk=1∞ k!·(x − 3)ᵏ/kᵏ.

Σ k!·(x − 3)ᵏ/kᵏx₀ = 3
R =
5.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 3 at x = 1.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₃|.

f(x) = cos xn = 3x = 1.5M = 1
|R₃| =
6.Hard

Find the coefficient c₄ of (x − 2)⁴ in the Taylor series of f(x) = ln x about a = 2.

f(x) = ln xa = 2k = 4
c₄ =

Answer key

  1. 1. S25 = 2075
  2. 2. S9 = 2.672
  3. 3. C: Σ (−1)ᵏ/√k
  4. 4. R = 2.718
  5. 5. |R₃| = 0.2109
  6. 6. c₄ = −0.01563

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