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

Find the term a40 of the arithmetic sequence −11, −15, −19, −23, …

a₁ = −11d = −4n = 40
a40 =
2.Easy
kak​123456

Find the sum S6 of the first 6 terms of the geometric sequence 10, 20, 40, …

a₁ = 10r = 2n = 6
S6 =
3.Medium
xx₀ = 2??R

The power series Σk=1∞ (x − 2)ᵏ/(k²·5ᵏ) converges on an interval around x₀ = 2. Find the right end x of that interval.

Σ (x − 2)ᵏ/(k²·5ᵏ)x₀ = 2
x =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ kᵏ/(3ᵏ·k!). Find L = lim |ak+1/ak|.

ak = kᵏ/(3ᵏ·k!)
L =
5.Hard
xyfP₄−1

Use the Maclaurin polynomial of degree 4 of f(x) = cos(2x) to approximate f(−1). Give P₄(−1).

f(x) = cos(2x)n = 4x = −1
P₄(−1) =
6.Hard

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

ak = (−1)ᵏ/(2k + 1)!
S =

Answer key

  1. 1. a40 = −167
  2. 2. S6 = 630
  3. 3. x = 7
  4. 4. L = 0.9061
  5. 5. P₄(−1) = −0.3333
  6. 6. S = 0.8415

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