Question

5^n+1 -2×5^n/3×5^n-2

Answer 1

$\frac{5^{n+1}-2\cdot5^n}{3\cdot5^{n-2}}= \frac{5^n\cdot5-2\cdot5^n}{3\cdot5^n\cdot5^{-2}}= \frac{5^n(5-2)}{3\cdot5^n\cdot5^{-2}}= \frac{1}{5^{-2}}= 5^2=5$

Answer 2

We can simplify the expression using algebraic manipulation as follows:

5^(n+1) - 25^n / (35^(n-2))

= 5^n5^1 - 25^n / (35^n5^(-2))

= 5^n5/5^2 - 2/35^(-2)

= 5^(n-1) - 2/3*1/25

= 5^(n-1) - 2/75

Therefore, the simplified form of the expression is 5^(n-1) - 2/75.