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
