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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Name: ____________________   Date: ____________

1.Easy
kak​12345678910

Find the sum S10 of the first 10 terms of the arithmetic sequence 1, 1.5, 2, 2.5, …

a₁ = 1d = 0.5n = 10
S10 =
2.Easy
kak​12345

Find the sum S5 of the first 5 terms of the geometric sequence 2, 4, 8, …

a₁ = 2r = 2n = 5
S5 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·2ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·2ᵏ/(2k)!
L =
4.Medium
AΣ 1/k³k = 1 … ∞BΣ (5/4)ᵏk = 1 … ∞CΣ 3ᵏ/k³k = 1 … ∞DΣ 1/√kk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 1/k³B: Σ (5/4)ᵏC: Σ 3ᵏ/k³D: Σ 1/√k
  1. 1A: Σ 1/k³
  2. 2B: Σ (5/4)ᵏ
  3. 3C: Σ 3ᵏ/k³
  4. 4D: Σ 1/√k
5.Hard

Recognise the series and find its sum: S = Σk=0∞ 0.5ᵏ/k!.

ak = 0.5ᵏ/k!
S =
6.Hard
xyfP₅2.5

Use the Maclaurin polynomial of degree 5 of f(x) = sin x to approximate f(2.5). Give P₅(2.5).

f(x) = sin xn = 5x = 2.5
P₅(2.5) =

Answer key

  1. 1. S10 = 32.5
  2. 2. S5 = 62
  3. 3. L = 0.5
  4. 4. A: Σ 1/k³
  5. 5. S = 1.649
  6. 6. P₅(2.5) = 0.7096

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