Help on arithemetic and geometric sequences?

Question

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 · Accepted 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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gripp · Answer

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 · Answer

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

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Help on arithemetic and geometric sequences?

3 Answers