Question

if each term of a G.P. is raised to the power x show that the resulting sequence is also a G.P.

Answer 1

Hope you got your answer

Answer 2

Answer:

The proof is explained step wise below :

Step-by-step explanation:

$\text{Let the G.P. be }a,a^r,a\cdot r^2,a\cdot r^3,......$

where the first term is a, and the common ratio is r.

If each term of the G.P. is raised to the power of x then the resulting sequence is :

$a^x,a^xr^x,a^xr^{2\cdot x},a^xr^{3\cdot x},...........\\\\So,\frac{a^xr^x}{a^x}=\frac{a^xr^{2\cdot x}}{a^xr^x}=\frac{a^xr^{3\cdot x}}{a^xr^{2\cdot x}}=r^x\\\\\text{which means that each term is obtained by multiplying the previous term with }\bf r^x\\\\\textbf{Thus, the resulting sequence is a G.P. with first term }a^x\\\textbf{and the common ratio }r^x$