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​123456789101112

Find the sum S35 of the first 35 terms of the arithmetic sequence 7, 4, 1, −2, …

a₁ = 7d = −3n = 35
S35 =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 10, 5, 2.5, …

a₁ = 10r = 0.5n = 9
S9 =
3.Medium
AΣ (−1)ᵏ/kk = 1 … ∞BΣ 3ᵏ/k²k = 1 … ∞CΣ 3/kk = 1 … ∞DΣ ln k / kk = 1 … ∞

Exactly one of the four series converges. Click it.

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

Find the sum S = Σk=1∞ 12/(k(k + 2)).

ak = 12/(k(k + 2))
S =
5.Hard

Recognise the series and find its sum: S = Σk=1∞ k·0.5ᵏ.

ak = k·0.5ᵏ
S =
6.Hard

f(x) = sin x is approximated at x = 2 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 1, find the smallest degree n that guarantees an error below 0.0001.

f(x) = sin xx = 2M = 1ε = 0.0001
n =

Answer key

  1. 1. S35 = −1540
  2. 2. S9 = 19.96
  3. 3. A: Σ (−1)ᵏ/k
  4. 4. S = 9
  5. 5. S = 2
  6. 6. n = 10

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