If , and are in geometric progression, then ^9 + ^6 +3 ^5 + ^3 + ^2 =

Step-by-step solution

, , are in geometric progression. aligned & = & = ^2 ^3 = ^2 .....(i) aligned aligned & Now, ^9 + ^6 +3 ^5 + ^3 + ^2 & = ^6 + ^6 +3 ^5 + ^2 + ^2 [from (i)] & = ( ^2 + ^2 ) ( ^4 + ^4 - ^2 ^2 )+3 & ^5 +1 & = ( ^2 + ^2 )^2-3 ^2 ^2 +3 ^5 +1 & =1^2-3 ^5 +3 ^5 +1=2 aligned