Question

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

Answer 1

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48/25 , 54/25, 60/25, 66/25, 72/25

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step-by-step explanation:

given,

the numbers are in A.P

now,

let the first number be 'a' and common diffrence bs 'd'

therefore,

a2 = a+d

a3 = a+2d

a4 = a+3d

a5 = a+4d

now,

given that,

their sum equals 12

=> 5a + 10d = 12 ..............(i)

also,

ratio of first to last equals 2:3

=> a/(a+4d) = 2/3

=> 3a = 2(a+4d)

=> 3a = 2a + 8d

=> a = 8d .................(ii)

putting the value of 'a' from eqn (ii) in eqn (i),

we get,

=> 5( 8d) + 10d = 12

=> 40d + 10d = 12

=> 50d = 12

=> d = 6/25

therefore,

a = 48/25

so,

the required numbers are,

48/25 , 54/25, 60/25, 66/25, 72/25