Nth term of -7 -6 -3 2 9 18 29

n^2 - 2n - 6.

Step-by-step explanation:

The difference between terms is

1 3 5 7 9 11  which is an arithmetic sequence with common difference 2.

The given series is quadratic and the nth term will contain n^2.

n       =        1       2     3      4     5

n^2   =        1       4    9    16    25

term  =      -7     -6    -3     2      9      Subtract these from the n^2 values:

Subtract:    8     10   12    14     16

The last row is an A.S. with  nth term   8 + 2(n - 1) =  6 + 2n

So the required nth term = n^2 - (6 + 2n)

= n^2 - 2n - 6.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

stops on an even number.