koli123able
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
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ANSWER = 2,4,6,8 OR 8,6,4,2
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koli123able
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Cant understand how to start
sauravshakya
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Let four numbers in AP be
a-3d ,a-d ,a+d and a+3d
sauravshakya
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Now,
a-3d+a-d+a+d+a+3d=20
4a=20
a=5
sauravshakya
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Also,
(a-3d)(a+3d)/ {(a-d) (a+d)} =2/3
koli123able
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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"
sauravshakya
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It simply means (a-3d)(a+3d)/ {(a-d) (a+d)} =2/3
koli123able
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oh
koli123able
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what should i do next.. cross multiply?
sauravshakya
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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
sauravshakya
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Now, can u?
koli123able
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ok
koli123able
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i have to substitute the values of a and d in the four numbers which were a-3d, and so on
sauravshakya
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yep
koli123able
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ok got the numbers :)
koli123able
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thanks
sauravshakya
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welcome