Question

Find the common second difference for the following sequence:
\[
-7 ;-15 ;-25 ;-37 ; \ldots
\]

Answer 1

Start by finding the first differences of the terms:
\[
\begin{array}{ll}
\text { For } T_{1} \text { and } T_{2}: & -15-(-7)=-8 \\
\text { For } T_{2} \text { and } T_{3}: & -25-(-15)=-10 \\
\text { For } T_{3} \text { and } T_{4}: & -37-(-25)=-12
\end{array}
\]
Now calculate the second differences:
\[
\begin{array}{ll}
\text { first two differences: } & -10-(-8)=-2 \\
\text { next two differences: } & -12-(-10)=-2
\end{array}
\]

 

In this case, the second differences are equal to each other, with a value of \(-2\).