Question

Divide 30 into Five parts an Ap such that first and last part is in the ratio 2:3.​

Answer 1

Solution

let five numbers in AP be a,a+d,a+2d,a+3d,a+4d

Then sum of all these parts equal 30

=)a+(a+d)+(a+2d)+(a+3d)+(a+4d)=30

=)5a+10d= 30

=) a+2d=6------(1)

Also the ratio of the first and last part 2:3

This implies that,

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

=) 3a= 2a+8d

=)3a-2a-8d= 0

=) a-8d=0---------(2)

Subtract (2) from (1)

=) a+2d=6

a-8d= 0

- + -

_____________

=) 10d= -6

=) d= -6/10

=)d= -0.6

put this value in (1) to get,

=) a+2(-0.6)= 6

=) a-1.2=6

=)a= 6+1.2

=)a= 7.2

So the required parts are

=) 7.2, 1.2, -4.8, -10.8, -16.8

hope it helps

Answer 2

here is your answer......