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

A ball is dropped and its first rebound reaches 10 m. Every next rebound reaches 85% of the previous one. Which rebound n is the first one lower than 0.5 m?

a₁ = 10r = 0.85ε = 0.5

n =

2.Easy

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

a = 5r = 1/2k₀ = 1

S =

3.Medium

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

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

S =

4.Medium

Find the sum S = Σ_k=1¹⁹ 12/(k(k + 1)).

a_k = 12/(k(k + 1))n = 19

S =

5.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 3 at x = −0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₃|.

f(x) = eˣn = 3x = −0.5M = 1

|R₃| =

6.Hard

Use the Maclaurin polynomial of degree 2 of f(x) = e^0.5x to approximate f(2). Give P₂(2).

f(x) = e^0.5xn = 2x = 2

P₂(2) =

Answer key

1. n = 20
2. S = 5
3. S = 3.125
4. S = 11.4
5. |R₃| = 0.002604
6. P₂(2) = 2.5

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