Question

For what positive value of p will this be a geometric sequence: p-3, p+1, 3p+3?

Answer 1

`p=5`

Explanation:

If `p-3, p+1, 3p+3` is a geometric sequence
then for some constant `c`:
`color(white)("XXX")color(red)((p-3)xxc=(p+1))`
and
`color(white)("XXX"color(blue)((p+1)xxc=3p+3)`

Therefore
`color(white)("XXX")color(blue)(((p+1)xxcancel(c)))/color(red)(((p-3)xxcancel(c)))=color(blue)((3p+3))/color(red)((p+1))=(3(cancel(p+1)))/(cancel(p+1))`

`color(white)("XXX")(p+1)/(p-3)=3`

`color(white)("XXX")p+1=3p-9`

`color(white)("XXX")-2p=-10`

`color(white)("XXX")p=5`