Posted by pavithra on Tuesday, March 12, 2013 at 7:01am.
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 - drwls, Tuesday, March 12, 2013 at 7:04am
What does AP mean and what does this have to do with Christ?
- CHRIST MATH - Reiny, Tuesday, March 12, 2013 at 9:50am
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)
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
(a-d)(a+4d) = 0
a = d or a = -4d
case1: a = d
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 - Reiny, Tuesday, March 12, 2013 at 10:00am
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
Answer This Question
More Related Questions
- Maths - Divide Rs 116 among 4 parts such that 5 added to first part 4 subtracted...
- math - PART A)find x using the ratio of the sides 12 cm and 16 cm: x/20=12/16. ...
- MATH - PART A)find x using the ratio of the sides 12 cm and 16 cm: x/20=12/16. ...
- maTH - PART A)find x using the ratio of the sides 12 cm and 16 cm: x/20=12/16. ...
- college math - in a conjecture the answer i got was 12n how would it look if it ...
- maths - divide 72 in to two parts such that one part is three times the other ...
- physics - A 9.3 kg firework is launched straight up and at its maximum height 45...
- maths-urgent - divide 44degree8minutes into two parts such that the number of ...
- mathematics - find the number in an A.P such that the sum of 1st and 3rd term is...
- Quantitative, stastics and business - A company has three machines A, B and C ...