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
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Find the sum S28 of the first 28 terms of the arithmetic sequence 7, 4, 1, −2, …

a₁ = 7d = −3n = 28
S28 =
2.Easy
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Find the sum S9 of the first 9 terms of the geometric sequence 4, 2, 1, …

a₁ = 4r = 0.5n = 9
S9 =
3.Medium
xx₀ = 1??R

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

Σ k²·2ᵏ·(x − 1)ᵏx₀ = 1
x =
4.Medium
xx₀ = −1??R

The power series Σk=1∞ 5ᵏ·(x + 1)ᵏ/(k + 1) converges on an interval around x₀ = −1. Find the left end x of that interval.

Σ 5ᵏ·(x + 1)ᵏ/(k + 1)x₀ = −1
x =
5.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 4 at x = −0.5. 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 = −0.5M = 1
|R₄| =
6.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 2 at x = 1. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e1 = 2.718 to find the largest possible error |R₂|.

f(x) = eˣn = 2x = 1M = 2.718
|R₂| =

Answer key

  1. 1. S28 = −938
  2. 2. S9 = 7.984
  3. 3. x = 1.5
  4. 4. x = −1.2
  5. 5. |R₄| = 0.0002604
  6. 6. |R₂| = 0.453

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