The explicit rule for an arithmetic sequence is an = -4 + (n - 1)7.

what is the common difference of the arithmetic sequence?
d =

The common difference of the arithmetic sequence is 7.

Step-by-step explanation:

The explicit rule for an arithmetic sequence is

           .... (1)

where, a is first term of an AP and d is common difference.

The given explicit rule for an arithmetic sequence is

             .... (2)

From (1) and (2), we get

It means the first term of the arithmetic sequence is -4 and the common difference is 7.

Therefore the common difference of the arithmetic sequence is 7.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .