Algebra 2 Equation of growth and decay, Equation of arithmetic sequence 
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*Why do I need a $1$ in this equation of growth and decay? $A=P(1\pm r)^t$ 

*Why must I divide by $2$ to find the sum of an arithmetic sequence?
$S(n) = \frac{n}{2}(a_1 + a_n)$ 

1) because  for $t=0$ we have $P=A$
2)because in the arithmetic sequence the addition of two terms equidistant from the extreme elements $a_1$ and $a_n$ is the same, and we have $n/2$ sums of this kind. 
