Question

find five number in ap whose sum is 12 and the ratio of the first to the last is 2:3 ​

Answer 1

sum of an AP is given by n/2 (2a + ( n-1) d)

since sum of first 5 term is given

so,

5/2(2a+4d) = 25/2

= a +2d =5/2--------(1)

and a/d = 2/3-----------(2)

so, I it value of a form (2) in (1)

= 2d/3+2d=5/2

so,

d=15/16 and a= 2d/3= 5/8

there fore first five numbers are

5/8, 25/10, 40/10 , 55/10, 70/10

Answer 2

Answer:

Step-by-step explanation:

Sum of  an AP is given by n/2 (2a+(n-1)d)

Siince sum of first 5 terms is given ∴ 5/2 (2a+4d)=25/2

= a+2d=5/2     ___(1)

and a/d=2/3 __(2)

∴ put value of a  from (2) in (1) we get 2d/3 +2d=5/2

∴d=15/16   and a=2d/3 =5/8

therefore first five numbers are a ,a+d,a+2d,a+3d,a+4d

5/8,25/16,40/16,55/16,70/16

Hope it helps you...