Posted by Miracle on Friday, February 14, 2014 at 6:13am.
The 1st term of a G.P is equal to x-2,the 3rd term is x+6 and the arithmetic mean of the 1st and 3rd terms stands in the ratio to the 2nd 5:3.find the value of x.
- Math.G.P - Reiny, Friday, February 14, 2014 at 9:28am
arithmetic mean of 1st and 3d
= (x-2 + x+6)/2
= (2x + 4)/2
let the 2nd be y
then y/(x-2) = (x+6)/y
y^2 = (x-2)(x-6)
y = ± √((x-2)(x+6))
mean:2nd = 5:3
(x+2)/√((x-2)(x+6)) = 5/3
square both sides and expand
(x^2 + 4x + 4)/(x^2 + 4x - 12) = 25/9
25x^2 + 100x - 300 = 9x^2 + 36x + 36
16x^2 + 64x - 336 = 0
x^2 + 4x - 21 = 0
(x+7)(x-3) = 0
x = -7 or x = 3
if x = -7,
the 3 terms are : -9, ±3, -1
(only the sequence -9, -3, -1 works)
if x = 3
the 3 terms are :1, ±3, 9
(only the sequence 1 , 3, 9 works)
so x = -7 or x = 3
Answer This Question
More Related Questions
- math - in a geometric sequence the first term is 2. The 3rd term is the sum of ...
- math - the 3rd term of a geometric progression is nine times the 1st term.if the...
- math - The sum of the 1st nine terms of an arithmetic series is 216. The 1st,3rd...
- math - The 10th term of an arithmetic progress in 28 and the 7th term is 19....
- arithmetic - THE SUM OF THE 2ND AND 5TH TERMS OF AN A.P IS 42. IF THE DIFFERENCE...
- arithmetic - An arithmetic n geometric sequence have the same first term 2.with ...
- Sequence - Find the common difference and a formula formula for the nth term of ...
- arithmetic - I have a Q that im trying to solve: it says: the 1st , 2nd, and 3rd...
- math - The 3rd term of a geometric progression is nine times the 1st term.if the...
- mathematics - find the number in an A.P such that the sum of 1st and 3rd term is...