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​123456

Find the sum S6 of the first 6 terms of the geometric sequence 5, 10, 20, …

a₁ = 5r = 2n = 6
S6 =
2.Easy
kak​135791113ε = 0.5

A ball is dropped and its first rebound reaches 3 m. Every next rebound reaches 85% of the previous one. Which rebound n is the first one lower than 0.5 m?

a₁ = 3r = 0.85ε = 0.5
n =
3.Medium
xx₀ = 3??R

The power series Σk=1∞ (x − 3)ᵏ/(k²·2ᵏ) converges on an interval around x₀ = 3. Find the left end x of that interval.

Σ (x − 3)ᵏ/(k²·2ᵏ)x₀ = 3
x =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 5/(k(k + 1)).

ak = 5/(k(k + 1))
S =
5.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 4 at x = 0.8. 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 = 0.8M = 1
|R₄| =
6.Hard

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

f(x) = sin xn = 3x = 1M = 1
|R₃| =

Answer key

  1. 1. S6 = 315
  2. 2. n = 13
  3. 3. x = 1
  4. 4. S = 5
  5. 5. |R₄| = 0.002731
  6. 6. |R₃| = 0.04167

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