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

1 Answer
Alan P.
Jan 16, 2016

#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#

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