SOLUTION: i have to find the rule for this step 1= 24 step 2= 22 step 3= 20 step 4= 18 step 5= 16 step 6= 14 step 7 =12

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Question 631694: i have to find the rule for this
step 1= 24
step 2= 22
step 3= 20
step 4= 18
step 5= 16
step 6= 14
step 7 =12

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
To get from 
step 1= 24
to
step 2= 22,
we have to subtract 2, so from the original 24 we have subtracted 2 1 time in step 2.
To get from
step 2= 22
to
step 3= 20,
we have to subtract 2, so from the original 24 we have subtracted 2 2 times in step 3.
To get from
step 3= 20 
to
step 4= 18,
we have to subtract 2, so from the original 24 we have subtracted 2 3 times in step 4.
To get from
step 4= 18
to
step 5= 16, 
we have to subtract 2, so from the original 24 we have subtracted 2 4 times in step 5. 
To get from
step 5= 16
to
step 6= 14, 
we have to subtract 2, so from the original 24 we have subtracted 2 5 times in step 6. 
To get from
step 6= 14
to
step 7= 12, 
we have to subtract 2, so from the original 24 we have subtracted 2 5 times in step 7. 
.
.
.
To get from
step n-1 = an-1
to
step n= an, 
we have to subtract 2, so from the original 24 we have subtracted 2 n-1 times in step n.
To get from
step n= an
to
step n+1= an+1 
we have to subtract 2, so from the original 24 we have subtracted 2 n times in step n+1.

Therefore the recursive formula is

a1 = 24, an+1 = an - 2 

and the general formula is

an = 24 - (n-1)·2

That can be simplified:

an = 24 - 2(n-1)

an = 24 - 2n + 2

an = 26 - 2n

an = 2(13 - n)

Edwin

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