Question

Write an explicit equation using function notation to represent the sequence:-2, -6, -10, -14,...

Answer 1

hello

since this requires an explicit equation we need to define some terms first

a = -2

common difference = -4

$F(n)=a+(n-1)d$

all we need to do is substitute the values of a and d into the equation above

$\begin{gathered} f(n)=a+(n-1)d \\ f(n)=-2+(n-1)\cdot-4 \\ f(n)=-2-4n+4 \\ f(n)=2-4n \end{gathered}$

the explicit equation for this series is 2 - 4n

test for f(3) and f(4)

$\begin{gathered} f(3)=2-4(3) \\ f(3)=2-12 \\ f(3)=10 \\ \\ \end{gathered}$$\begin{gathered} f(4)=2-4(4) \\ f(4)=2-16 \\ f(4)=-14 \end{gathered}$