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​12345

Find the sum S5 of the first 5 terms of the geometric sequence 10, 30, 90, …

a₁ = 10r = 3n = 5
S5 =
2.Easy
kak​123456789101112

The arithmetic sequence 0, 5, 10, 15, … ends with the term 85. How many terms n does it have?

a₁ = 0d = 5aₙ = 85
n =
3.Medium
xx₀ = 1??R

Find the radius of convergence R of the power series Σk=1∞ (x − 1)ᵏ/(k·5ᵏ).

Σ (x − 1)ᵏ/(k·5ᵏ)x₀ = 1
R =
4.Medium
xx₀ = −2??R

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

Σ (2k)!·(x + 2)ᵏ/(k!)²x₀ = −2
x =
5.Hard
xyfP₃−0.4

Use the Maclaurin polynomial of degree 3 of f(x) = 1/(1 − x) to approximate f(−0.4). Give P₃(−0.4).

f(x) = 1/(1 − x)n = 3x = −0.4
P₃(−0.4) =
6.Hard

f(x) = cos 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) = cos xn = 4x = −0.5M = 1
|R₄| =

Answer key

  1. 1. S5 = 1210
  2. 2. n = 18
  3. 3. R = 5
  4. 4. x = −2.25
  5. 5. P₃(−0.4) = 0.696
  6. 6. |R₄| = 0.0002604

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