Question

apply geometric progression solve in details

Answer 1

Given,

First term ( a ) = 2^( n -1 ).

Common ratio ( r ) = 2^( n - 2 ) ÷ 2^( n - 1 )

                       = 2^( n - 2 - n + 1 )

                      = 2^( - 1 ).


Last term ( l ) = 2^0 = 1.


There is a formula to find the sum of a G.P by using first term , last term and common ratio only.

Sum of n terms = ( a - lr ) ÷ ( 1 - r )

                       
 = { 2^( n - 1 ) - 1 ( 2^-1 )} ÷ ( 1 - 2^-1 )

= { 2^( n - 1 ) - 2^( - 1 ) } ÷ ( 1 - 1/2 )

= { 2^-1 ( 2^n - 1 )  } ÷ ( 1/2 )

= { ( 1/2 ) ( 2^n  - 1 ) } ÷ ( 1/2 )

= 2^n - 1.

Answer 2

Hey mate!

Here's your answer!!

It's in the attachment file.

Hope it helps you!!!