Given that the sum of the first n terms of the provided series is 6560 determine the value of n (2,6,18,54.)

n = 8

Step-by-step explanation:

The given sequence, 2, 6, 18, 54. . ., is a geometric sequence.

It has a common ratio of 3 =>

Thus, the sum of the first n terms of a geometric sequence is given as

Where,

= first term of the series = 2

r = common ratio = 3

= sum of the first n terms = 6,560

Plug in the above values into the formula

Multiply both sides by -1

Subtract 1 from both sides

Evaluate

3 cancels 3

The value of n = 8

the co-ordinates of the transformed rectangle are:

d. (0, 0), (0, 3), (-3, 3), (-3, 0)

step-by-step explanation:

from the columns of the given matrix, the co-ordinates of the rectangle before transformation are:

(0, 0), (0, 3), (3, 3), (3, 0)

r =

transformed matrix can be obtained by multiplying the given matrix by r:

columns of the transformed matrix are:

0   0   -3   -3

0   3     3     0

from the columns of the resulted matrix, we can see that the vertices of the transformed triangle are:

(0, 0), (0, 3), (-3, 3), (-3, 0)

its 50 miles away from the starting point