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​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 0.5, 1.5, 4.5, …

a₁ = 0.5r = 3n = 9
S9 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 10·(1/3)ᵏ.

a = 10r = 1/3k₀ = 0
S =
3.Medium
xx₀ = 2??R

The power series Σk=1∞ (1/2)ᵏ·(x − 2)ᵏ/(k + 1) converges on an interval around x₀ = 2. Find the right end x of that interval.

Σ (1/2)ᵏ·(x − 2)ᵏ/(k + 1)x₀ = 2
x =
4.Medium
AΣ 3ᵏ/k!k = 1 … ∞BΣ (−1)ᵏ/kk = 1 … ∞CΣ 1/(2ᵏ + k)k = 1 … ∞DΣ (k + 4)/k²k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 3ᵏ/k!B: Σ (−1)ᵏ/kC: Σ 1/(2ᵏ + k)D: Σ (k + 4)/k²
  1. 1A: Σ 3ᵏ/k!
  2. 2B: Σ (−1)ᵏ/k
  3. 3C: Σ 1/(2ᵏ + k)
  4. 4D: Σ (k + 4)/k²
5.Hard

Find the coefficient c₄ of (x − 2)⁴ in the Taylor series of f(x) = ln x about a = 2.

f(x) = ln xa = 2k = 4
c₄ =
6.Hard
xyfP₅0.8

Use the Maclaurin polynomial of degree 5 of f(x) = sin(3x) to approximate f(0.8). Give P₅(0.8).

f(x) = sin(3x)n = 5x = 0.8
P₅(0.8) =

Answer key

  1. 1. S9 = 4921
  2. 2. S = 15
  3. 3. x = 4
  4. 4. D: Σ (k + 4)/k²
  5. 5. c₄ = −0.01563
  6. 6. P₅(0.8) = 0.7596

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