Question

Geometric Progression Answer fast please .........

Answer 1

a( m + n ) = ar^ ( m + n - 1 ) = p

a( m - n ) = ar^( m - n - 1 ) = q

Dividing both equations,

p / q = [ ar^ ( m + n - 1 ) ] / [ ar^ ( m - n - 1 ) ]

p/ q = r ^( m + n - 1 - m + n + 1 )

p / q = r^ ( 2n )

r = ( p/ q) ^ 1/ 2n

1 / r = ( q / p ) ^ 1/2n

am = ar^ ( m - 1 )

am = a r^ ( m + n - 1 ) ( 1/ r ) ^n

am = a ( m +n ) ( 1/r ) ^ n

am = p ( q/p )^( n/ 2n)

$<h4>am = p ( q / p) ^ 1/2 = √pq</h4>$

an = ar^( n - 1 )

an = ar^( m+n - 1 ) ( 1/r ) ^m

an = a ( m + n ) ( 1/ r ) ^m

$<h4> an = p ( q / p ) m / 2n </h4>$

Answer 2

Please see the attachment