anonymous
  • anonymous
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
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Cant understand how to start
anonymous
  • anonymous
Let four numbers in AP be a-3d ,a-d ,a+d and a+3d
anonymous
  • anonymous
Now, a-3d+a-d+a+d+a+3d=20 4a=20 a=5

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anonymous
  • anonymous
Also, (a-3d)(a+3d)/ {(a-d) (a+d)} =2/3
anonymous
  • anonymous
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"
anonymous
  • anonymous
It simply means (a-3d)(a+3d)/ {(a-d) (a+d)} =2/3
anonymous
  • anonymous
oh
anonymous
  • anonymous
what should i do next.. cross multiply?
anonymous
  • anonymous
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
anonymous
  • anonymous
Now, can u?
anonymous
  • anonymous
ok
anonymous
  • anonymous
i have to substitute the values of a and d in the four numbers which were a-3d, and so on
anonymous
  • anonymous
yep
anonymous
  • anonymous
ok got the numbers :)
anonymous
  • anonymous
thanks
anonymous
  • anonymous
welcome

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