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
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 3·(−1/3)ᵏ.

a = 3r = −1/3k₀ = 1
S =
2.Easy
kak​123456789101112

Find the term a19 of the arithmetic sequence 15, 20, 25, 30, …

a₁ = 15d = 5n = 19
a19 =
3.Medium
xx₀ = 1??R

The power series Σk=1∞ k²·4ᵏ·(x − 1)ᵏ converges on an interval around x₀ = 1. Find the right end x of that interval.

Σ k²·4ᵏ·(x − 1)ᵏx₀ = 1
x =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ xᵏ/5ᵏ.

Σ xᵏ/5ᵏx₀ = 0
R =
5.Hard

Find the coefficient c₄ of (x − 1)⁴ in the Taylor series of f(x) = 1/x about a = 1.

f(x) = 1/xa = 1k = 4
c₄ =
6.Hard
xyfP₄0.5

Use the Maclaurin polynomial of degree 4 of f(x) = cos(3x) to approximate f(0.5). Give P₄(0.5).

f(x) = cos(3x)n = 4x = 0.5
P₄(0.5) =

Answer key

  1. 1. S = −0.75
  2. 2. a19 = 105
  3. 3. x = 1.25
  4. 4. R = 5
  5. 5. c₄ = 1
  6. 6. P₄(0.5) = 0.08594

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