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

Find the sum S34 of the first 34 terms of the arithmetic sequence 19, 21, 23, 25, …

a₁ = 19d = 2n = 34
S34 =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 4, 4.8, 5.76, …

a₁ = 4r = 1.2n = 9
S9 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k²·3ᵏ/5ᵏ. Find L = lim |ak+1/ak|.

ak = k²·3ᵏ/5ᵏ
L =
4.Medium
xx₀ = 0??R

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

Σ xᵏ/(1/2)ᵏx₀ = 0
R =
5.Hard

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

f(x) = √xa = 1k = 4
c₄ =
6.Hard

f(x) = ln(1 + x) is approximated by its Maclaurin polynomial of degree 4 at x = 0.1. 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 = 0.1M = 24
|R₄| =

Answer key

  1. 1. S34 = 1768
  2. 2. S9 = 83.2
  3. 3. L = 0.6
  4. 4. R = 0.5
  5. 5. c₄ = −0.03906
  6. 6. |R₄| = 2 × 10⁻⁶

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