Question

Find the constant second difference for the following sequence:
\[
7 ; 4 ;-3 ;-14 ; \ldots
\]

Answer 1

Start by finding the first differences of the terms:
\[
\begin{array}{ll}
\text { For } T_{1} \text { and } T_{2}: & 4-(7)=-3 \\
\text { For } T_{2} \text { and } T_{3}: & -3-(4)=-7 \\
\text { For } T_{3} \text { and } T_{4}: & -14-(-3)=-11
\end{array}
\]
Now calculate the second differences:
\[
\begin{array}{ll}
\text { first two differences: } & -7-(-3)=-4 \\
\text { next two differences: } & -11-(-7)=-4
\end{array}
\]
 

In this case, the second differences are equal to each other, with a value of \(-4\).