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

The arithmetic sequence 6, 10, 14, 18, … ends with the term 66. How many terms n does it have?

a₁ = 6d = 4aₙ = 66
n =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 9·(−2/3)ᵏ.

a = 9r = −2/3k₀ = 2
S =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = (k!)²·1ᵏ/(2k)!
L =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 3ᵏ·xᵏ/(k + 1).

Σ 3ᵏ·xᵏ/(k + 1)x₀ = 0
R =
5.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 3 at x = 0.2. 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 = 0.2M = 1
|R₃| =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·1.22k/(2k)!.

ak = (−1)ᵏ·1.22k/(2k)!
S =

Answer key

  1. 1. n = 16
  2. 2. S = 2.4
  3. 3. L = 0.25
  4. 4. R = 0.3333
  5. 5. |R₃| = 6.667 × 10⁻⁵
  6. 6. S = 0.3624

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