The sum of 3 numbers in A.P. is 15. If we add 1, 4, 19 respectively, then the new numbers form a G.P. Find the numbers of the A.P.

Answer

N/a

Explanation

Let three numbers in A.P. be a-d, a, a+d.
`therefore" "a-d+a+a+d=15`
`rArr" "3a=15`
`rArr" "a=5`
Therefore, numbers are 5-d, 5, 5+d Add 1, 4, 19 respectively in these numbers.
`"Now, numbers 6 - d, 9, 24 + d form a G.P."`
`therefore" "(9)^(2)=(6-d)(24+d)`
`rArr" "81=144-18d-d^(2)`
`rArr" "d^(2)+18d-63=0`
`rArr" "(d+21)(d-3)=0`
`rArr" "d=-21`
`"or "d=3`


`a=5,d=-21,"then numbers are 26, 5, - 16."`
`a=5,d=3,"then numbers are 2, 5, 8."`