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 14, 17, 20, 23, … ends with the term 68. How many terms n does it have?

a₁ = 14d = 3aₙ = 68
n =
2.Easy
kak​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 0.5, 0.75, 1.125, …

a₁ = 0.5r = 1.5n = 7
S7 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k³·2ᵏ/5ᵏ. Find L = lim |ak+1/ak|.

ak = k³·2ᵏ/5ᵏ
L =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = 2ᵏ·k!/kᵏ
L =
5.Hard
xyfP₂0.25

Use the Maclaurin polynomial of degree 2 of f(x) = ln(1 + 2x) to approximate f(0.25). Give P₂(0.25).

f(x) = ln(1 + 2x)n = 2x = 0.25
P₂(0.25) =
6.Hard
xyfP₄2.5

Use the Maclaurin polynomial of degree 4 of f(x) = eˣ to approximate f(2.5). Give P₄(2.5).

f(x) = eˣn = 4x = 2.5
P₄(2.5) =

Answer key

  1. 1. n = 19
  2. 2. S7 = 16.09
  3. 3. L = 0.4
  4. 4. L = 0.7358
  5. 5. P₂(0.25) = 0.375
  6. 6. P₄(2.5) = 10.86

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