Question

sum of 3 numbers which are ap is 27 .if we add 1,3and 11 to them respectively the numbers are obtained in gp .find the number

Answer 1

Answer:

Step-by-step explanation:

Let the numbers which are in A.P be (a-d), a, (a+d) where a is the first term and d is the common difference between them.

Now,

a-d+a+a+d=27

3a=27

a=27/3

a=9

Again,

(a+3)/(a-d+1)= (a+d+11) / (a+3)

(a+3)(a+3)= (a+d+11)(a-d+1)

(9+3)(9+3)=(9+d+11)(9-d+1)

144=(d+20)(10-d)

144=200-10d-d^2

d^2+10d+144-200=0

d^2+10d-56=0

d^2+14d-4d-56=0

d(d+14)-4(d+14)=0

(d+14)(d-4)=0

Either,                                                  Or,

d+14=0                                        d-4=0

d=-14                                            d=4

When d=-14,                         When d=4,

1st no=a-d=9+14=23              1st no=a-d=9-4=5

2nd no=a=9                              2nd no=a=9

3rd no=a+d=9-14=-5                3rd no=a+d=9+4=13