Answer to Question #315624 in Algebra for HEND

Question

A geometric progression has a second term of 12 and a sum to infinity of 54. Find the possible values of the first term of the progression

Answer 1

$ar=12, \;\frac{a}{1-r}=54.$

$r=\frac{12}{a},\;\frac{a^2}{a-12}=54.$

$a^2-54a+648=0.$

$a=18,\;a=36.$