Question

The sequence an = one third (3)n - 1 is graphed below: Find the average rate of change between n = 3 and n = 4.

Answer 1

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array} \\\\\\ \begin{cases} x_1=3\\ x_2=4 \end{cases}\implies \cfrac{f(4)-f(3)}{4-3}\implies \cfrac{9-3}{4-3}\implies \cfrac{6}{1}\implies 6$