Question

what is the second difference for the table below.

a 3
b -2
c 1
d 4

Explanation:

Step1: Calculate the first differences

The first difference is calculated as \(g(x + 1)-g(x)\).
For \(x=-1\) to \(x = 0\): \(40 - 58=-18\)
For \(x = 0\) to \(x=1\): \(25 - 40=-15\)
For \(x = 1\) to \(x=2\): \(13 - 25=-12\)
For \(x = 2\) to \(x=3\): \(4 - 13=-9\)
For \(x = 3\) to \(x=4\): \(-2 - 4=-6\)

Step2: Calculate the second differences

The second difference is calculated as (first difference at \(x + 1\))-(first difference at \(x\)).
\((-15)-(-18)=3\)
\((-12)-(-15)=3\)
\((-9)-(-12)=3\)
\((-6)-(-9)=3\)

Answer:

A. 3