CHRIST MATH
posted by pavithra .
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

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

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)/(a^2 + 3ad + 2d^2) = 2/3
3a^2 + 9ad = 2a^2 + 6ad + 4d^2 = 0
a^2 + 3ad  4d^2 = 0
(ad)(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 
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
Respond to this Question
Similar Questions

physics
A 9.3 kg firework is launched straight up and at its maximum height 45 m it explodes into three parts. Part A (0.5 kg) moves straight down and lands 0.29 seconds after the explosion. Part B (1 kg) moves horizontally to the right and … 
Maths
Divide Rs 116 among 4 parts such that 5 added to first part 4 subtracted from the second part 3 mutltiplied by third part and fourth part divided by 2 are all equal 
maths
divide 72 in to two parts such that one part is three times the other part 
maTH
PART A)find x using the ratio of the sides 12 cm and 16 cm: x/20=12/16. Show your work PART B) find x using the ratio of the sides 6 cm and 8 cm. Show your work PART C) Explain why the answers to a and b should be the same The triangles … 
MATH
PART A)find x using the ratio of the sides 12 cm and 16 cm: x/20=12/16. Show your work PART B) find x using the ratio of the sides 6 cm and 8 cm. Show your work PART C) Explain why the answers to a and b should be the same The triangles … 
math
PART A)find x using the ratio of the sides 12 cm and 16 cm: x/20=12/16. Show your work PART B) find x using the ratio of the sides 6 cm and 8 cm. Show your work PART C) Explain why the answers to a and b should be the same The triangles … 
college math
in a conjecture the answer i got was 12n how would it look if it was to be part Amultiplied by 12 part Badd 12 to the product Part C divide the sum by 2 PArt Dsubtract 6 from the quotient 
math
divide 95m long string such that twice of 1st part, 4 times of 2nd part and 5 times of 3rd part are equals 
Maths
Divide 8 into 2 parts such that 7 times the square of the smaller part exceeds twoce the square of the other part by 13 
Algebra
Divide 105 in two parts such that 1 third of one part is equal to 1 forth of other part