Sunday

September 21, 2014

September 21, 2014

Posted by **pavithra** on Tuesday, March 12, 2013 at 7:01am.

- CHRIST MATH -
**drwls**, Tuesday, March 12, 2013 at 7:04amWhat does AP mean and what does this have to do with Christ?

- CHRIST MATH -
**Reiny**, Tuesday, March 12, 2013 at 9:50amI 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

(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 -
**Reiny**, Tuesday, March 12, 2013 at 10:00amI 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**

**Related Questions**

calculus - 1st digit is square root of 2nd digit 2nd digit is square of 1st sum ...

Math.G.P - The 1st term of a G.P is equal to x-2,the 3rd term is x+6 and the ...

Help! - I am stumped with a problem we are supposed to help our 4th grader with...

science - Is venus the 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th or 9th smallest ...

math - Identify -7x^3+6x^2+6x+9 1st, 2nd, 3rd, and 4th terms. Thanks

Math/Standard and scientific notation - Express each measure in standard form. (...

math - 6 runners run in a 500 yard dash. Prizes are awarded for 1st, 2nd, and ...

maths-urgent - divide 44degree8minutes into two parts such that the number of ...

arithmetic - I have a Q that im trying to solve: it says: the 1st , 2nd, and 3rd...

programming - I need a help regarding this. Compute and display the sum o 1st ...