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​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 3, 6, 12, …

a₁ = 3r = 2n = 7
S7 =
2.Easy
kak​12345

Find the sum S5 of the first 5 terms of the geometric sequence 5, 2.5, 1.25, …

a₁ = 5r = 0.5n = 5
S5 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·3ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·3ᵏ/(2k)!
L =
4.Medium
AΣ 1/(k(k + 4))k = 1 … ∞BΣ (−1)ᵏ/√kk = 1 … ∞CΣ (2/3)ᵏk = 1 … ∞DΣ 1/(4k + 6)k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 1/(k(k + 4))B: Σ (−1)ᵏ/√kC: Σ (2/3)ᵏD: Σ 1/(4k + 6)
  1. 1A: Σ 1/(k(k + 4))
  2. 2B: Σ (−1)ᵏ/√k
  3. 3C: Σ (2/3)ᵏ
  4. 4D: Σ 1/(4k + 6)
5.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ/(2k)!.

ak = (−1)ᵏ/(2k)!
S =
6.Hard
xyfP₄2

Use the Maclaurin polynomial of degree 4 of f(x) = cos(−x) to approximate f(2). Give P₄(2).

f(x) = cos(−x)n = 4x = 2
P₄(2) =

Answer key

  1. 1. S7 = 381
  2. 2. S5 = 9.688
  3. 3. L = 0.75
  4. 4. D: Σ 1/(4k + 6)
  5. 5. S = 0.5403
  6. 6. P₄(2) = −0.3333

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