Find a85 of the sequence 4,9,14,19,

424

Step-by-step explanation:

Since the difference between consecutive terms are constant, that is

19 - 14 = 14 - 9 = 9 - 4 = 5 ← common difference (d)

Then these are the terms of an arithmetic sequence with n th term

= a₁ + (n - 1)d

where a₁ is the first term = 4 and d the common difference, hence

= 4 + (84 × 5) = 4 + 420 = 424

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: