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​13579111315ε = 0.5

The geometric sequence aₙ = 10·0.8ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.5.

a₁ = 10r = 0.8ε = 0.5
n =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 24·(−1/3)ᵏ.

a = 24r = −1/3k₀ = 2
S =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 4/(k(k + 4)).

ak = 4/(k(k + 4))
S =
4.Medium
AΣ (−1)ᵏ/kk = 1 … ∞BΣ (1 + 1/k)ᵏk = 1 … ∞CΣ (k + 3)/k²k = 1 … ∞DΣ (3/2)ᵏk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (−1)ᵏ/kB: Σ (1 + 1/k)ᵏC: Σ (k + 3)/k²D: Σ (3/2)ᵏ
  1. 1A: Σ (−1)ᵏ/k
  2. 2B: Σ (1 + 1/k)ᵏ
  3. 3C: Σ (k + 3)/k²
  4. 4D: Σ (3/2)ᵏ
5.Hard

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1·0.25ᵏ/k.

ak = (−1)k+1·0.25ᵏ/k
S =
6.Hard
xyfP₅2

Use the Maclaurin polynomial of degree 5 of f(x) = sin x to approximate f(2). Give P₅(2).

f(x) = sin xn = 5x = 2
P₅(2) =

Answer key

  1. 1. n = 15
  2. 2. S = 2
  3. 3. S = 2.083
  4. 4. A: Σ (−1)ᵏ/k
  5. 5. S = 0.2231
  6. 6. P₅(2) = 0.9333

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