Given the sequence: 2x-3, 7x, 11x; find x if the sequence is arithmetic and then geometric.
I already have the answers which are -3 for arithmetic and -11/9 for geometric, but I don't understand how to do this. If anyone can help me out without being rude, it would be greatly appreciated.
Wayne DeguMan
Favorite Answer
Arithmetic series
=> 7x - (2x - 3) = 11x - 7x
so, 5x + 3 = 4x
=> x = -3
Geometric series
=> 7x/(2x - 3) = 11x/7x
so, 7x/(2x - 3) = 11/7
=> 7(7x) = 11(2x - 3)
i.e. 49x = 22x - 33
=> 27x = -33
i.e. x = -33/27 = -11/9
Not rude but to the point!
:)>
Mawuena Corsy-Dewu
For an arithmetic sequence, the difference between successive terms is a constant, usually referred to as the 'common difference' which I denote by the letter 'd'. From the sequence you've stated;
7x - (2x-3) = d and also 11x - 7x = d
therefore 7x - (2x-3) = 11x - 7x
7x - 2x + 3 = 4x
5x - 4x = -3
x = -3
For a geometric sequence, the ratio between successive terms is a constant referred to as the 'common ratio' which I denote by the letter 'r'. From your given sequence;
7x/(2x-3) = r and 11x/7x = r
therefore 7x/(2x-3) = 11x/7x
(7x) x (7x) = (11x) x (2x-3)
49x^2 = 22x^2 -33x
49x^2 - 22x^2 = -33x
27x^2 = -33x
x^2/x = -33/27
x = -11/9
?
I can help you out if it is arithmetic
what is the difference between the 2nd and 3nd term?
11x-7x = 4x and the difference between 2nd and 1st 7x-(2x-3) = 5x+3 the differences should be the same so 4x=5x+3
and -x=3 and x=-3
geometric progression is
y(2x-3) = 7x and 7xy = 11x then set those two equal and solve
y= 7x / (2x-3 and y = 11x / 7x or y = 11/7 substitute into first equation
11/7 = 7x / (2x-3) cross multiply
11(2x-3) = 49x
22x - 33 = 49x
-33 = 27x
x= -33/27 or - 11/9
Robert Cotton
Arithmetic: there is constant number added from one term to the next so
(7x)-(2x-3)=(11x)-(7x)
5x+3=4x
x=-3
Geometric: there is a constant number multiplied from one term to the next so
(7x)/(2x-3)=(11x)/(7x)
(7x)(7x)=(2x-3)(11x)
49x^2=22x^2-33x
27x^2+33x=0
(3x)(9x+11)=0
3x=0 or 9x+11=0
x=0 or x=-11/9 but it not work for the x=0 so it is only x=-11/9