Question

Insert two numbers between 3 and 81 so that the resulting sequence is G.P.

Answer 1

We b and c be the numbers between 3 and 81. 

a-3, b = ar = 3r, c = ar²  = 3r²  and d = ar³  = 3r³  = T₄ 

But T₄ = ar^4-1 = 3r³ 

⇒ 81 = 3r³ 

⇒ r³  = 27 = 3³ 

⇒ r = 3

∴ b = ar = 3 x 3 = 9

and c = ar²  = 3 x 3²  = 27