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
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 18·(−3/4)ᵏ.

a = 18r = −3/4k₀ = 1
S =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 1, 3, 9, …

a₁ = 1r = 3n = 9
S9 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 4/(k(k + 1)).

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

Exactly one of the four series converges. Click it.

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

Recognise the series and find its sum: S = Σk=1∞ k·0.2ᵏ.

ak = k·0.2ᵏ
S =
6.Hard
xyfP₄1.5

Use the Maclaurin polynomial of degree 4 of f(x) = cos(−x) to approximate f(1.5). Give P₄(1.5).

f(x) = cos(−x)n = 4x = 1.5
P₄(1.5) =

Answer key

  1. 1. S = −7.714
  2. 2. S9 = 9841
  3. 3. S = 4
  4. 4. C: Σ (−1)ᵏ/k
  5. 5. S = 0.3125
  6. 6. P₄(1.5) = 0.08594

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