## Acalytica

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

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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 $-4$.

by Diamond (78,219 points)

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