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 S12 of the first 12 terms of the arithmetic sequence 10, 6, 2, −2, …

a₁ = 10d = −4n = 12
S12 =
2.Easy
kak​123456789101112

Find the sum S27 of the first 27 terms of the arithmetic sequence 0, −2, −4, −6, …

a₁ = 0d = −2n = 27
S27 =
3.Medium
AΣ (k + 5)/k²k = 1 … ∞BΣ (−1)ᵏ/kk = 1 … ∞CΣ 1/√kk = 1 … ∞DΣ (7/4)ᵏk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (k + 5)/k²B: Σ (−1)ᵏ/kC: Σ 1/√kD: Σ (7/4)ᵏ
  1. 1A: Σ (k + 5)/k²
  2. 2B: Σ (−1)ᵏ/k
  3. 3C: Σ 1/√k
  4. 4D: Σ (7/4)ᵏ
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 5/(k(k + 1)).

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

f(x) = cos 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 0.0005.

f(x) = cos xx = 2M = 1ε = 0.0005
n =
6.Hard

Find the coefficient c₃ of (x + 1)³ in the Taylor series of f(x) = eˣ about a = −1.

f(x) = eˣa = −1k = 3
c₃ =

Answer key

  1. 1. S12 = −144
  2. 2. S27 = −702
  3. 3. B: Σ (−1)ᵏ/k
  4. 4. S = 5
  5. 5. n = 9
  6. 6. c₃ = 0.06131

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