Question

The sum of three numbers in ap is 15. If 1, 4, 19 are to be added to them respectively, the results are in GP. The numbers are

Answer 1

ur answer is in pic.......
hope it helps u

Answer 2

Answer:

The numbers are 26, 5, -16 and 2, 5, 8.

Step-by-step explanation:

The sum of three numbers, which are in A.P., can be written as:

a – d, a, a + d  

Using Sum of A.P., we get;

a – d + a + a + d = 15

a = 5

By putting a = 5 we get    5 – d, a, 5 + d  

Now as question said adding 1, 4, 19 we get  

1+5 – d, 4+a, 5 + d+19

6 – d, 4 + a, 24 + d

As the Difference is same, we get

$\begin{array}{l}{\frac{9}{6-d}=\frac{24+d}{9}} \\ {144+6 d-24 d-d^{2}=81} \\ {d^{2}+18 d-63=0}\end{array}$

d(d+21)-3(d+21)

(d+21)(d-3)    

We get d = -21 and d = 3

By putting d = -21  in   5 – d, a, 5 + d  

we get  

5 – (-21), 5, 5 + (-21)  =  26, 5, -16

And if d = 3

We get

5 – (3), 5, 5 + (3)  = 2, 5, 8