Let a₁, a₂, a₃, be a G. P. of increasing positive numbers. If a ₃ a ₅=729 and a ₂+ a ₄= 111 4 , then 24 (a₁+a₂+a₃ ) is equal to

Step-by-step solution

Let the I ^ st term of G.P. be a & common ratio be r aligned a ₃ a ₅ & = ar ^2 ar ^4=729 & = a ^2 r ^6=729 & = ar ^3=27 ....(i) aligned aligned a ₂+ a ₄ & = ar + ar ^3= 111 4 & = ar = 3 4 ....(ii) aligned (i) (ii) aligned & ar ^3 ar = 27 3 / 4 & r ^2=36 & r =6 aligned from (ii) a(6)= 3 4 a= 1 8 Now, 24 (a₁+a₂+a₃ ) aligned & =24 (a+a r+a^2 ) & =24 a (1+r+r^2 ) aligned aligned & =24 1 8 (1+6+36) & =3(43) & =129 aligned