Ap gp

Since it is given that the first three numbers forms an A.P.

 

Let the these three numbers be a - d, a , a + d.

 

a - d + a + d = 2   ... given

→ a = 1

 

Since it is given that the last three numbers forms an G.P.

 

Let the these three numbers be a, ar  and ar² .

 

a + ar² = 26  ... given

→a (1 + r²) = 26

→ r² = 25

→ r = ± 5

The numbers are a - d , a , a + d = ar , ar².

 

a + d = ar 

→ 1 + d = 1 × ±5 

→ d = 4 or d = -6

When a= 1 and d = 4 and r = 5 then the numbers will be  -3, 1, 5, 25

and when a= 1 and d = -6 and r = -5 then the numbers will be  7, 1, -5, 25