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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Name: ____________________   Date: ____________

1.Easy
kak​123456

Find the sum S6 of the first 6 terms of the geometric sequence 2, 4, 8, …

a₁ = 2r = 2n = 6
S6 =
2.Easy
kak​123456789101112

Find the sum S15 of the first 15 terms of the arithmetic sequence −9, −5, −1, 3, …

a₁ = −9d = 4n = 15
S15 =
3.Medium
xx₀ = −2??R

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

Σ k!·(x + 2)ᵏ/kᵏx₀ = −2
x =
4.Medium
k|aₖ|¹ᐟᵏ123456789101112

Apply the root test to Σk=1∞ ((2k + 3)/(3k + 1))ᵏ. Find L = lim |ak|1/k.

ak = ((2k + 3)/(3k + 1))ᵏ
L =
5.Hard

Recognise the series and find its sum: S = Σk=1∞ k·0.2ᵏ.

ak = k·0.2ᵏ
S =
6.Hard

Find the coefficient c₂ of (x − 1)² in the Taylor series of f(x) = ln x about a = 1.

f(x) = ln xa = 1k = 2
c₂ =

Answer key

  1. 1. S6 = 126
  2. 2. S15 = 285
  3. 3. x = −4.718
  4. 4. L = 0.6667
  5. 5. S = 0.3125
  6. 6. c₂ = −0.5

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