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 S36 of the first 36 terms of the arithmetic sequence 16, 18, 20, 22, …

a₁ = 16d = 2n = 36
S36 =
2.Easy
kak​123456789101112

Find the sum S37 of the first 37 terms of the arithmetic sequence −1, −0.5, 0, 0.5, …

a₁ = −1d = 0.5n = 37
S37 =
3.Medium
AΣ 1/(4k + 7)k = 1 … ∞BΣ k/5ᵏk = 1 … ∞CΣ 1/k⁴k = 1 … ∞DΣ (3/5)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 1/(4k + 7)B: Σ k/5ᵏC: Σ 1/k⁴D: Σ (3/5)ᵏ
  1. 1A: Σ 1/(4k + 7)
  2. 2B: Σ k/5ᵏ
  3. 3C: Σ 1/k⁴
  4. 4D: Σ (3/5)ᵏ
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 5/(k(k + 4)).

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

f(x) = eˣ is approximated at x = 1 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 3, find the smallest degree n that guarantees an error below 0.001.

f(x) = eˣx = 1M = 3ε = 0.001
n =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·0.82k+1/(2k + 1)!.

ak = (−1)ᵏ·0.82k+1/(2k + 1)!
S =

Answer key

  1. 1. S36 = 1836
  2. 2. S37 = 296
  3. 3. A: Σ 1/(4k + 7)
  4. 4. S = 2.604
  5. 5. n = 6
  6. 6. S = 0.7174

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