SOLUTION: What is the general term for sequence 2, -4, 8, -16, 32, ...

n    term



1     2

2     -2*2 = -4

3     -2*-4 = 8 = -2*-2*2

4     -2*8 = -16 = (-2)^3 * 2

5     -2*-16 = 32 = (-2)^4 * 2




Do you see the pattern for the n'th term?    

What you see, is a geometric progression with the first term 2 and the common ratio of -2.


Notice that due to the fact that the common ratio is negative, the terms change their sign from "+" to "-" and from "-" to "+".


The general term is   =  = .



You may check it, by calculating first terms using this formula.

    For our valuable visitors, it is hopeless to expect that they 

    will guess the formula: for the first time, they should see it . . . 

    They should see it, when they meet such problem for the first time.


    And it is very normal situation.


    We should be thankful to god, if they will understand our explanations,
    after seeing the direct demonstration for the first time . . . 


        It is my personal view to this educational subject.


    And, depending on their age (and the personal mental features), they may need to see such direct demonstration

    even SEVERAL times (more that once) . . .