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
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 4·(2/5)ᵏ.

a = 4r = 2/5k₀ = 1
S =
2.Easy
kak​123456789101112

Find the sum S31 of the first 31 terms of the arithmetic sequence 9, 11.5, 14, 16.5, …

a₁ = 9d = 2.5n = 31
S31 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·2ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·2ᵏ/(2k)!
L =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 3/(k(k + 2)).

ak = 3/(k(k + 2))
S =
5.Hard

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

f(x) = √xa = 1k = 2
c₂ =
6.Hard
xyfP₅2.5

Use the Maclaurin polynomial of degree 5 of f(x) = sin(−x) to approximate f(2.5). Give P₅(2.5).

f(x) = sin(−x)n = 5x = 2.5
P₅(2.5) =

Answer key

  1. 1. S = 2.667
  2. 2. S31 = 1442
  3. 3. L = 0.5
  4. 4. S = 2.25
  5. 5. c₂ = −0.125
  6. 6. P₅(2.5) = −0.7096

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