# CHRIST MATH

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Divide 20 into 4 parts which are in AP such that ratio between the product of the 1st part and the 4th part to the 2nd and 3rd part is 2:3 find the AP

• CHRIST MATH -

What does AP mean and what does this have to do with Christ?

• CHRIST MATH -

I will assume that AP stands for arithmetic progression

so you are given:
a + (a+d) + (a+2d) + (a+3d) = 20
4a + 6d = 20
2a + 3d = 10

product of 1st and 4th = a(a+3d)
product of 2nd to 3rd = (a+d)(a+2d)

then:
a(a+3d)/( (a+d)(a+2d) ) = 2/3
a^2 + 3ad - 4d^2 = 0
(a-d)(a+4d) = 0

a = d or a = -4d

case1: a = d
in 2a+3d=10
5d = 10,
d = 2, so a=d = 2
the terms are 2, 4, 6 , 8

case2: a = 4d
in 2a + 3d = 10
-4d + 3d = 10
-d = 10
d = -10, then a = 40
the terms are 40, 30, 20, 10

• typo - CHRIST MATH -

I just noticed a typo in my second case
It should say:

case2: a = -4d
in 2a + 3d = 10
-8d + 3d = 10
-2d = 10
d = -5, then a = 20
the terms are 20 , 15, 10 , 5

but these do not add up to 20 , even though the ratio of product property works

so the only solution are the terms

2, 4, 6, 8

notice they add up to 20
and (2x8)/(4x6) = 16/24 = 2/3