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

The arithmetic sequence 10, 7, 4, 1, … ends with the term −83. How many terms n does it have?

a₁ = 10d = −3aₙ = −83
n =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 2, −4, 8, …

a₁ = 2r = −2n = 9
S9 =
3.Medium
AΣ 1/(2ᵏ + k)k = 1 … ∞BΣ 3/kk = 1 … ∞CΣ 3/k³k = 1 … ∞DΣ (−1)ᵏ/√kk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 1/(2ᵏ + k)B: Σ 3/kC: Σ 3/k³D: Σ (−1)ᵏ/√k
  1. 1A: Σ 1/(2ᵏ + k)
  2. 2B: Σ 3/k
  3. 3C: Σ 3/k³
  4. 4D: Σ (−1)ᵏ/√k
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 4/(k(k + 3)).

ak = 4/(k(k + 3))
S =
5.Hard

Find the coefficient c₂ of (x − 2)² in the Taylor series of f(x) = 1/x about a = 2.

f(x) = 1/xa = 2k = 2
c₂ =
6.Hard

f(x) = cos x is approximated at x = 1 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 1 × 10⁻⁶.

f(x) = cos xx = 1M = 1ε = 1 × 10⁻⁶
n =

Answer key

  1. 1. n = 32
  2. 2. S9 = 342
  3. 3. B: Σ 3/k
  4. 4. S = 2.444
  5. 5. c₂ = 0.125
  6. 6. n = 9

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