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

Elise Kelley

Elise Kelley

Answered question

2022-10-23

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

Answer & Explanation

Kaylee Evans

Kaylee Evans

Beginner2022-10-24Added 20 answers

If p−3, p+1, 3p+3 is a geometric sequence
then for some constant c:
XXX ( p - 3 ) × c = ( p + 1 )
and
XXX ( p + 1 ) × c = 3 p + 3
Therefore
XXX ( ( p + 1 ) × c ) ( ( p - 3 ) × c ) = ( 3 p + 3 ) ( p + 1 ) = 3 ( p + 1 ) p + 1
XXX p + 1 p - 3 = 3
XXX p + 1 = 3 p - 9
XXX - 2 p = - 10
XXX p = 5

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