Question

If 6, 6^x + 2, and 6^3x - 3 are the first three terms of a geometric sequence, what is the value of x?

Answer 1

\[\frac{6^x+2}{6}=\frac{6^{3x}-3}{6^x+2}\] is a start

Answer 2

its to 6 to the power of x+2

Answer 3

ok then i guess you need to solve this
\[\frac{6^{x+2}}{6}=\frac{6^{3x}-3}{6^{x+2}}\]

Answer 4

or perhaps
\[\frac{6^{x+2}}{6}=\frac{6^{3x-3}}{6^{x+2}}\]

Answer 5

so its going to be x+2= 2x-5

Answer 6

and then x= -3

Answer 7

it is going to be
\[6^{x+2}\times 6^{x+2}=6^{2x+4}=6\times 6^{3x-3}=6^{3x-2}\]

Answer 8

so \[2x+4=3x-2\]

Answer 9

so x=6

Answer 10

that is what i get, yes