Question

Three numbers are in AP. Their sum is 15. If 1, 4and19 are added to them they become in GP. Find the numbers.



pls help very urgent

Answer 1

let a,b,c be the numbers in AP.

Then,2b = a+c

Given,their sum = 15

So, a+b+c = 2b +b=15

3b = 15

b= 5 ; a+ c =10.

Also , Given that , a + 1 , b + 4 , c +19 are in gp

If three numbers x,y,z are in GP , then y^2 =xz

So,here 

(b+4)^2 = (a + 1) (c + 19)

81 = ac + 19 + c + 19a

19a + c + ac = 62

19a + 10 -a + a(10 - a) =62

28a - a^2 = 52

a^2 -28a +52 = 0

a^2 - 26a -2a +52 = 0
a(a - 26) -2 (a - 26 ) =0

(a-2)(a-26) =0

a = 2 or 26

If a = 2 , b= 5 , c= 10 -2 =8

If a = 26 , b= 5 ,c = 10-26 = -16

So numbers are (2,5,8) ,(26,5,-16)

Hope this helps !

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Answer 2

a-d,a,a+d
cond: 1
a-d+a+a+d=15
3a=15
a=15/3
a=3