Question

three numbers are are in G.P whose sum is 70 if the extreme be each multiplied by 4 and the mean by 5 they will be in A.P the numbers are

Answer 1

let the 3 nos be a , ar and ar²
given that the sum of no's is 70
there for a(1+r+r²) =70 ....................................................(i)

also given that 4a,5ar and 4ar² in AP
⇒2(5ar)=4a+4ar²
⇒5r=2+2r²
⇒2r²-5r+2=0

r=2 or 1/2

from(i) we get
a=10  at r=2
and a =40 at r=1/2

where a=10 and r=2 , the numbers are 10, 20, ,40

and when a=40 and r =1/2
the numbers are 40,20,10

hence the numbers are 10,20,40

Answer 2

Step-by-step explanation:

a+ar+ar^2=70

extremes = a and ar^2

mean=ar

4a+5ar+4ar^2

In AP

{2b=a+c}

2*5ar=4a+4ar^2

5r=2+2r^2

2r^2-5r+2r=0

r=2,1/2

r=2 r=1/2

a+2a+4a=70 a+a/2+a/4=70

7a=70 7a=280

a=10 a=40

a= 10 , 40

ar= 20 , 20

ar^2=40 , 10