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 −3, −2.5, −2, −1.5, … ends with the term 9.5. How many terms n does it have?

a₁ = −3d = 0.5aₙ = 9.5
n =
2.Easy
kak​123456789101112

Find the term a23 of the arithmetic sequence −9, −4, 1, 6, …

a₁ = −9d = 5n = 23
a23 =
3.Medium
xx₀ = 2??R

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

Σ k!·(x − 2)ᵏ/kᵏx₀ = 2
x =
4.Medium
AΣ (k + 3)/k²k = 1 … ∞BΣ 1/(k(k + 4))k = 1 … ∞CΣ k!/10ᵏk = 1 … ∞DΣ k/(k + 2)k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (k + 3)/k²B: Σ 1/(k(k + 4))C: Σ k!/10ᵏD: Σ k/(k + 2)
  1. 1A: Σ (k + 3)/k²
  2. 2B: Σ 1/(k(k + 4))
  3. 3C: Σ k!/10ᵏ
  4. 4D: Σ k/(k + 2)
5.Hard

Recognise the series and find its sum: S = Σk=1∞ k·0.25ᵏ.

ak = k·0.25ᵏ
S =
6.Hard
xyfP₃1.5

Use the Maclaurin polynomial of degree 3 of f(x) = sin x to approximate f(1.5). Give P₃(1.5).

f(x) = sin xn = 3x = 1.5
P₃(1.5) =

Answer key

  1. 1. n = 26
  2. 2. a23 = 101
  3. 3. x = 4.718
  4. 4. B: Σ 1/(k(k + 4))
  5. 5. S = 0.4444
  6. 6. P₃(1.5) = 0.9375

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