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=0∞ 4·(−2/3)ᵏ.

a = 4r = −2/3k₀ = 0
S =
2.Easy
kak​12345678910

Find the sum S10 of the first 10 terms of the geometric sequence 10, 15, 22.5, …

a₁ = 10r = 1.5n = 10
S10 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 4)).

ak = 1/(k(k + 4))
S =
4.Medium
AΣ 2ᵏ/k³k = 1 … ∞BΣ (5k + 1)/(k + 2)k = 1 … ∞CΣ 1/(2ᵏ + k)k = 1 … ∞DΣ (5/4)ᵏk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 2ᵏ/k³B: Σ (5k + 1)/(k + 2)C: Σ 1/(2ᵏ + k)D: Σ (5/4)ᵏ
  1. 1A: Σ 2ᵏ/k³
  2. 2B: Σ (5k + 1)/(k + 2)
  3. 3C: Σ 1/(2ᵏ + k)
  4. 4D: Σ (5/4)ᵏ
5.Hard
xyfP₄−0.5

Use the Maclaurin polynomial of degree 4 of f(x) = e3x to approximate f(−0.5). Give P₄(−0.5).

f(x) = e3xn = 4x = −0.5
P₄(−0.5) =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ 1.5ᵏ/k!.

ak = 1.5ᵏ/k!
S =

Answer key

  1. 1. S = 2.4
  2. 2. S10 = 1133
  3. 3. S = 0.5208
  4. 4. C: Σ 1/(2ᵏ + k)
  5. 5. P₄(−0.5) = 0.2734
  6. 6. S = 4.482

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