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 S19 of the first 19 terms of the arithmetic sequence 10, 8, 6, 4, …

a₁ = 10d = −2n = 19
S19 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 24·(2/5)ᵏ.

a = 24r = 2/5k₀ = 2
S =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k!/kᵏ. Find L = lim |ak+1/ak|.

ak = k!/kᵏ
L =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k³·3ᵏ/4ᵏ. Find L = lim |ak+1/ak|.

ak = k³·3ᵏ/4ᵏ
L =
5.Hard

Find the coefficient c₂ of (x − 3)² in the Taylor series of f(x) = ln x about a = 3.

f(x) = ln xa = 3k = 2
c₂ =
6.Hard

Find the coefficient c₄ of (x − 1)⁴ in the Taylor series of f(x) = ∛x about a = 1.

f(x) = ∛xa = 1k = 4
c₄ =

Answer key

  1. 1. S19 = −152
  2. 2. S = 6.4
  3. 3. L = 0.3679
  4. 4. L = 0.75
  5. 5. c₂ = −0.05556
  6. 6. c₄ = −0.04115

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