Given a,b,c are in A.P.,b,c,d are in G.P and c,d,e are in H.P .If a=2 and e=18 , then the sum of all possible value of c is ________.

Answer

0

Explanation

a,b,c are in A.P. `rArrb=(a+c)/2`
b,c,d are in G.P.
`rArrc^(2)=bd`
and c,d,e are in H.P.
`rArrd=(2ce)/(c+e)`
Now `c^(2)=bd`
or `c^(2)=((a+c)/2)((2ce)/(c+e))` [using (1) and (3)]
`thereforec^(2)+ce=ae+ce`
or `c^(2)=ae`
Now given a=2 and e=18
`thereforec^(2)=ae`
or `c^(2)=2xx18=36`
`rArrc=6 or -6`