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​12345678

Find the sum S8 of the first 8 terms of the geometric sequence 5, 2.5, 1.25, …

a₁ = 5r = 0.5n = 8
S8 =
2.Easy
kak​123456789101112

Find the sum S17 of the first 17 terms of the arithmetic sequence 13, 11, 9, 7, …

a₁ = 13d = −2n = 17
S17 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 5/(k(k + 1)).

ak = 5/(k(k + 1))
S =
4.Medium
xx₀ = 1??R

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

Σ k!·(x − 1)ᵏ/kᵏx₀ = 1
x =
5.Hard
xyfP₃2.5

Use the Maclaurin polynomial of degree 3 of f(x) = sin(0.5x) to approximate f(2.5). Give P₃(2.5).

f(x) = sin(0.5x)n = 3x = 2.5
P₃(2.5) =
6.Hard
xyfP₃1.5

Use the Maclaurin polynomial of degree 3 of f(x) = sin x to approximate f(1.5). Give P₃(1.5).

f(x) = sin xn = 3x = 1.5
P₃(1.5) =

Answer key

  1. 1. S8 = 9.961
  2. 2. S17 = −51
  3. 3. S = 5
  4. 4. x = −1.718
  5. 5. P₃(2.5) = 0.9245
  6. 6. P₃(1.5) = 0.9375

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