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 term a22 of the arithmetic sequence 4, 6.5, 9, 11.5, …

a₁ = 4d = 2.5n = 22
a22 =
2.Easy
kak​123456789101112

Find the sum S20 of the first 20 terms of the arithmetic sequence 3, 8, 13, 18, …

a₁ = 3d = 5n = 20
S20 =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ k²·3ᵏ·xᵏ.

Σ k²·3ᵏ·xᵏx₀ = 0
R =
4.Medium
AΣ ln k / kk = 1 … ∞BΣ 5ᵏ/k!k = 1 … ∞CΣ 3/k³k = 1 … ∞DΣ (2/3)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ ln k / kB: Σ 5ᵏ/k!C: Σ 3/k³D: Σ (2/3)ᵏ
  1. 1A: Σ ln k / k
  2. 2B: Σ 5ᵏ/k!
  3. 3C: Σ 3/k³
  4. 4D: Σ (2/3)ᵏ
5.Hard

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1/k.

ak = (−1)k+1/k
S =
6.Hard
xyfP₄0.8

Use the Maclaurin polynomial of degree 4 of f(x) = e3x to approximate f(0.8). Give P₄(0.8).

f(x) = e3xn = 4x = 0.8
P₄(0.8) =

Answer key

  1. 1. a22 = 56.5
  2. 2. S20 = 1010
  3. 3. R = 0.3333
  4. 4. A: Σ ln k / k
  5. 5. S = 0.6931
  6. 6. P₄(0.8) = 9.966

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