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

Find the sum S₈ of the first 8 terms of the geometric sequence 10, 8, 6.4, …

a₁ = 10r = 0.8n = 8

S₈ =

2.Easy

Find the term a₂₀ of the arithmetic sequence 5, 10, 15, 20, …

a₁ = 5d = 5n = 20

a₂₀ =

3.Medium

Find the sum S = Σ_k=1^∞ 6/(k(k + 4)).

a_k = 6/(k(k + 4))

S =

4.Medium

Apply the ratio test to Σ_k=1^∞ k!/kᵏ. Find L = lim |a_k+1/a_k|.

a_k = k!/kᵏ

L =

5.Hard

f(x) = cos x is approximated at x = 2 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 0.0005.

f(x) = cos xx = 2M = 1ε = 0.0005

n =

6.Hard

f(x) = cos x is approximated at x = 0.5 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 0.0001.

f(x) = cos xx = 0.5M = 1ε = 0.0001

n =

Answer key

1. S₈ = 41.61
2. a₂₀ = 100
3. S = 3.125
4. L = 0.3679
5. n = 9
6. n = 5

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