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 1, 1.5, 2.25, …

a₁ = 1r = 1.5n = 5
S5 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 6·(4/5)ᵏ.

a = 6r = 4/5k₀ = 2
S =
3.Medium
k|aₖ|¹ᐟᵏ123456789101112

Apply the root test to Σk=1∞ ((4k + 4)/(5k + 3))ᵏ. Find L = lim |ak|1/k.

ak = ((4k + 4)/(5k + 3))ᵏ
L =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 12/(k(k + 1)).

ak = 12/(k(k + 1))
S =
5.Hard

Find the coefficient c₃ of (x − 1)³ in the Taylor series of f(x) = √x about a = 1.

f(x) = √xa = 1k = 3
c₃ =
6.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 2 at x = 1.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₂|.

f(x) = sin xn = 2x = 1.5M = 1
|R₂| =

Answer key

  1. 1. S5 = 13.19
  2. 2. S = 19.2
  3. 3. L = 0.8
  4. 4. S = 12
  5. 5. c₃ = 0.0625
  6. 6. |R₂| = 0.5625

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