If ( log _{7}^{2}, 7^{log }left(e^{x}-5right), 7^{log _{7}left(2^{2}-frac{7}{2}right)} ) are in geometric progression then the sum of the possible values

If ( log _{7}^{2}, 7^{log }left(e^{x}-5right), 7^{log _{7}left(2^{2}-frac{7}{2}right)} ) are in geometric progression then the sum of the possible values

z=\frac{1}{4}x^{2}+\sin\left(\pi-x\right)\ -\frac{3}{4}y+\frac{abc}{\cos\left(x\right)}

Simplify the expression. Write your answer as a power.$\left(\left(-\frac{3}{4}\right)^5\right)^2$((−34​)5)2​The simplified expression is .

For what values of the common ratio r is it possible to find the sum of an infinite geometric series? (Enter your answer using interval notation.)−1x1

In a geometric progression, the sum of the first n terms is 3069 and the first term is 3. If the nth term in the progression is 1536, find the common ratio