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​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 4, −12, 36, …

a₁ = 4r = −3n = 9
S9 =
2.Easy
kak​123456789101112

The arithmetic sequence 18, 22, 26, 30, … ends with the term 146. How many terms n does it have?

a₁ = 18d = 4aₙ = 146
n =
3.Medium
AΣ 5ᵏ/k!k = 1 … ∞BΣ (−1)ᵏ/kk = 1 … ∞CΣ k!/10ᵏk = 1 … ∞DΣ 2/k⁴k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 5ᵏ/k!B: Σ (−1)ᵏ/kC: Σ k!/10ᵏD: Σ 2/k⁴
  1. 1A: Σ 5ᵏ/k!
  2. 2B: Σ (−1)ᵏ/k
  3. 3C: Σ k!/10ᵏ
  4. 4D: Σ 2/k⁴
4.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = (k!)²·1ᵏ/(2k)!
L =
5.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·0.52k+1/(2k + 1)!.

ak = (−1)ᵏ·0.52k+1/(2k + 1)!
S =
6.Hard

f(x) = ln(1 + x) is approximated by its Maclaurin polynomial of degree 4 at x = 0.2. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 4! = 24 to find the largest possible error |R₄|.

f(x) = ln(1 + x)n = 4x = 0.2M = 24
|R₄| =

Answer key

  1. 1. S9 = 19684
  2. 2. n = 33
  3. 3. C: Σ k!/10ᵏ
  4. 4. L = 0.25
  5. 5. S = 0.4794
  6. 6. |R₄| = 6.4 × 10⁻⁵

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