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​123456789

The arithmetic sequence 20, 21.5, 23, 24.5, … ends with the term 32. How many terms n does it have?

a₁ = 20d = 1.5aₙ = 32
n =
2.Easy
kak​123456789101112

Find the sum S18 of the first 18 terms of the arithmetic sequence 18, 20, 22, 24, …

a₁ = 18d = 2n = 18
S18 =
3.Medium
xx₀ = 3??R

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

Σ (2k)!·(x − 3)ᵏ/(k!)²x₀ = 3
x =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·5ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·5ᵏ/(2k)!
L =
5.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 3 at x = 0.8. 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 = 0.8M = 1
|R₃| =
6.Hard
xyfP₂1

Use the Maclaurin polynomial of degree 2 of f(x) = cos x to approximate f(1). Give P₂(1).

f(x) = cos xn = 2x = 1
P₂(1) =

Answer key

  1. 1. n = 9
  2. 2. S18 = 630
  3. 3. x = 2.75
  4. 4. L = 1.25
  5. 5. |R₃| = 0.01707
  6. 6. P₂(1) = 0.5

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