Answer:
[tex] \frac{133}{8} [/tex]
Step-by-step explanation:
Given,
[tex] {( \frac{5}{2} )}^{x} + {( \frac{5}{2} )}^{x + 3} [/tex]
[tex] = {( \frac{5}{2}) }^{x} + {( \frac{5}{2}) }^{x} \times {( \frac{5}{2} )}^{3} [/tex]
[tex] = ( \frac{5}{2} ) ^{x} (1 + {( \frac{5}{2} )}^{3} [/tex]
[tex] = {( \frac{5}{2} )}^{x} (1 + \frac{125}{8} )[/tex]
[tex] = {( \frac{5}{2} )}^{x} ( \frac{1 \times 8 + 125}{8} )[/tex]
[tex] = {( \frac{5}{2}) }^{x} ( \frac{8 + 125}{8} )[/tex]
[tex] {( \frac{5}{2} )}^{x} ( \frac{133}{8} )[/tex]
Comparing with A • [tex] {( \frac{5}{2}) }^{x} [/tex]
A = [tex] \frac{133}{8} [/tex]
Hope this helps...
Good luck on your assignment...
