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​123456789101112

The arithmetic sequence 1, 4, 7, 10, … ends with the term 103. How many terms n does it have?

a₁ = 1d = 3aₙ = 103
n =
2.Easy
kak​12345

Find the sum S5 of the first 5 terms of the geometric sequence 3, −9, 27, …

a₁ = 3r = −3n = 5
S5 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ kᵏ/(5ᵏ·k!). Find L = lim |ak+1/ak|.

ak = kᵏ/(5ᵏ·k!)
L =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 4/(k(k + 4)).

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

f(x) = ln(1 + x) is approximated by its Maclaurin polynomial of degree 4 at x = 0.2. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 4! = 24 to find the largest possible error |R₄|.

f(x) = ln(1 + x)n = 4x = 0.2M = 24
|R₄| =
6.Hard

Find the coefficient c₂ of (x − 2)² in the Taylor series of f(x) = e3x about a = 2.

f(x) = e3xa = 2k = 2
c₂ =

Answer key

  1. 1. n = 35
  2. 2. S5 = 183
  3. 3. L = 0.5437
  4. 4. S = 2.083
  5. 5. |R₄| = 6.4 × 10⁻⁵
  6. 6. c₂ = 1815

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