## koli123able 2 years ago The sum of four numbers in A.P is 20. The ratio of the product of the first and the last numbers and the product of 2nd & 3rd numbers is 2:3 ; Find the numbers . . . ANSWER = 2,4,6,8 OR 8,6,4,2

1. koli123able

Cant understand how to start

2. sauravshakya

Let four numbers in AP be a-3d ,a-d ,a+d and a+3d

3. sauravshakya

Now, a-3d+a-d+a+d+a+3d=20 4a=20 a=5

4. sauravshakya

Also, (a-3d)(a+3d)/ {(a-d) (a+d)} =2/3

5. koli123able

i cant understand this sentence "The ratio of the product of the first and the last numbers and the product of 2nd & 3rd numbers is 2:3"

6. sauravshakya

It simply means (a-3d)(a+3d)/ {(a-d) (a+d)} =2/3

7. koli123able

oh

8. koli123able

what should i do next.. cross multiply?

9. sauravshakya

Now, 3(a-3d)(a+3d) =2(a-d)(a+d) 3a^2 -27d^2 =2a^2 -2d^2 a^2 =25d^2 Also a=5 5^2 =25d^2 d^2=1 d=+-1

10. sauravshakya

Now, can u?

11. koli123able

ok

12. koli123able

i have to substitute the values of a and d in the four numbers which were a-3d, and so on

13. sauravshakya

yep

14. koli123able

ok got the numbers :)

15. koli123able

thanks

16. sauravshakya

welcome