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​123456789101112

Find the sum S22 of the first 22 terms of the arithmetic sequence −12, −7, −2, 3, …

a₁ = −12d = 5n = 22
S22 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 12·(4/5)ᵏ.

a = 12r = 4/5k₀ = 2
S =
3.Medium
AΣ 1/kk = 1 … ∞BΣ (1/2)ᵏk = 1 … ∞CΣ 3ᵏ/k!k = 1 … ∞DΣ 1/(k² + 4)k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 1/kB: Σ (1/2)ᵏC: Σ 3ᵏ/k!D: Σ 1/(k² + 4)
  1. 1A: Σ 1/k
  2. 2B: Σ (1/2)ᵏ
  3. 3C: Σ 3ᵏ/k!
  4. 4D: Σ 1/(k² + 4)
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 25ᵏx²ᵏ/k.

Σ 25ᵏx²ᵏ/kx₀ = 0
R =
5.Hard

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1·0.5ᵏ/k.

ak = (−1)k+1·0.5ᵏ/k
S =
6.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 4 at x = −0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₄|.

f(x) = cos xn = 4x = −0.5M = 1
|R₄| =

Answer key

  1. 1. S22 = 891
  2. 2. S = 38.4
  3. 3. A: Σ 1/k
  4. 4. R = 0.2
  5. 5. S = 0.4055
  6. 6. |R₄| = 0.0002604

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