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=1∞ 12·(4/5)ᵏ.

a = 12r = 4/5k₀ = 1
S =
2.Easy
kak​123456789101112

Find the term a20 of the arithmetic sequence −9, −7, −5, −3, …

a₁ = −9d = 2n = 20
a20 =
3.Medium
AΣ (3/4)ᵏk = 1 … ∞BΣ 1/k²k = 1 … ∞CΣ (5/4)ᵏk = 1 … ∞DΣ 1/(3ᵏ + k)k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (3/4)ᵏB: Σ 1/k²C: Σ (5/4)ᵏD: Σ 1/(3ᵏ + k)
  1. 1A: Σ (3/4)ᵏ
  2. 2B: Σ 1/k²
  3. 3C: Σ (5/4)ᵏ
  4. 4D: Σ 1/(3ᵏ + k)
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 4)).

ak = 1/(k(k + 4))
S =
5.Hard

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

ak = 2ᵏ/k!
S =
6.Hard

f(x) = ln(1 + x) is approximated by its Maclaurin polynomial of degree 3 at x = 0.2. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 3! = 6 to find the largest possible error |R₃|.

f(x) = ln(1 + x)n = 3x = 0.2M = 6
|R₃| =

Answer key

  1. 1. S = 48
  2. 2. a20 = 29
  3. 3. C: Σ (5/4)ᵏ
  4. 4. S = 0.5208
  5. 5. S = 7.389
  6. 6. |R₃| = 0.0004

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