Question

an geometric sequences is given as (x+40),(x+4),(x-20),...find the common ratio,r

Answer 1

3 points...x+40, x+4, x-20

distans tween points: 36, 24

24/36=2/3

maebee distans tween terms=(2/3)*prior term

Answer 2

If this is a GP, then the terms can be represented as a, ar, ar^2.

So a=x+40; ar=x+4; ar^2=x-20.

From the first two equations: ar/a=(x+4)/(x+40)=r; from the second pair of equations: r=(x-20)/(x+4). Therefore, (x+4)/(x+40)=(x-20)/(x+4). We can find x from this new equation: cross-multiply: (x+4)^2=(x+40)(x-20). Expand the brackets: x^2+8x+16=x^2+20x-800; 816=12x, so x=816/12=68. r=(x+4)/(x+40)=(x-20)/(x+4)=72/108 or 48/72=2/3.

Therefore, r=2/3 (and a=108 and x=68, making the series: 108, 72, 48).