Question

find five numbers in a gp such that their product is one and their sum of middle three is 13/3

Answer 1

Answer:

let nos be ar‐²,ar-¹,a,ar,ar²

ar‐²*ar-¹*a*ar*ar²=1

a⁵=1 so a=1

ar‐¹+a+ar=13/3

r-¹+1+r=13/3

1/r+r=10/3

(r²+1)/r=10/3

3r²-10r+3=0

solving the equation we get r =3 or 1/3

so the gp is 1/9,1/3,1,3,9