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​12345

Find the sum S5 of the first 5 terms of the geometric sequence 4, −12, 36, …

a₁ = 4r = −3n = 5
S5 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 2·(−1/4)ᵏ.

a = 2r = −1/4k₀ = 1
S =
3.Medium
xx₀ = 3??R

Find the radius of convergence R of the power series Σk=1∞ (x − 3)ᵏ/2ᵏ.

Σ (x − 3)ᵏ/2ᵏx₀ = 3
R =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 6/(k(k + 4)).

ak = 6/(k(k + 4))
S =
5.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 4 at x = −0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₄|.

f(x) = eˣn = 4x = −0.5M = 1
|R₄| =
6.Hard
xyfP₄2.5

Use the Maclaurin polynomial of degree 4 of f(x) = eˣ to approximate f(2.5). Give P₄(2.5).

f(x) = eˣn = 4x = 2.5
P₄(2.5) =

Answer key

  1. 1. S5 = 244
  2. 2. S = −0.4
  3. 3. R = 2
  4. 4. S = 3.125
  5. 5. |R₄| = 0.0002604
  6. 6. P₄(2.5) = 10.86

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