Find the explicit formula that produces the given sequence

Question

2,-6,18,-54........ Help please

Answer 1

There are two ways to look at the explicit formula:  either what the formula is, given the prior term, or the formula for any term.  

 

Suppose the sequence was this - 

 

5, -10, 20, -40, 80

 

You can see that it starts at 5, and then each successive term is multiplied by -2.

 

So, the formula for the next term is F(X+1) = -2*F(X)

and the formula for the first term is F(1) = 5

 

So we might guess that the formula was 

F(X) = 5 * (-2)^X

 

However, if we drop in an example (X=2) , we'd get F(2) =  20, which is really the third term, so we need to either reduce the exponent by 1 or divide the formula by -2.

 

F(X) = 5 * (-2)^(x-1) = -2.5 * (-2)^X

 

F(2) = -2.5 * 4 = -10 

 

So, that's the process.  Apply it to your initial sequence and you should get the right answer.