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Find the common second difference for the following sequence:
$-13 ;-25 ;-43 ;-67 ; \ldots$
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Start by finding the first differences of the terms:
\begin{aligned} &\text { For } T_{1} \text { and } T_{2}: \quad-25-(-13)=-12 \\ &\text { For } T_{2} \text { and } T_{3}: \quad-43-(-25)=-18 \\ &\text { For } T_{3} \text { and } T_{4}: \quad-67-(-43)=-24 \end{aligned}
Now calculate the second differences:
$\begin{array}{ll} \text { first two differences: } & -18-(-12)=-6 \\ \text { next two differences: } & -24-(-18)=-6 \end{array}$

In this case, the second differences are equal to each other, with a value of $-6$.

by Diamond (66,975 points)

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