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.
Jacinta
Favorite Answer
1. If it's arithmetic, then 7x - (2x - 3) = 11x - 7x
7x - 2x + 3 = 4x
5x + 3 = 4x
x + 3 = 0
x = -3
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2. If it's geometric, then 7x/(2x - 3) = 11x/7x
Simplify the right-hand side:
7x/(2x - 3) = 11/7
Cross-multiply:
49x = 11(2x - 3)
49x = 22x - 33
49x - 22x = -33
27x = -33
x = -33/27
x = -11/9
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<edit> Just thinking – I probably didn't explain clearly enough ...
In an arithmetic sequence, there's a COMMON DIFFERENCE between the terms. The difference between the first two terms is the same as the difference between the second two terms, hence equation #1 above.
In a geometric sequence, there's a COMMON RATIO between the terms. The ratio between the first two terms is the same as the ratio between the second two terms, hence equation #2.
This explains everything :)
http://www.mathsisfun.com/algebra/sequences-series.html
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?
First take the adjustments, 40 8, 24, 12,... they do no longer seem to be consistent so it is not arithmetic Now see if there's a basic ratio, ninety six/40 8 = 2, 40 8/24 = 2, .... sure so the sequence is geometric.
Anonymous
Arithmetic
Call 7x. a
Call 2x -3. a - d
Call 11x. a + d
Use simultaneous equations to find x.
Geometric
Call 7x. a
Call 2x -3. a/r
Call 11x. ar^2
Again just solve the three equations