`bar(jk)` is dilated by a scale factor of n with the origin as the center of dilation, resulting in the image `bar(j'k')`. the slope of `bar(jk)` is m. if the length of `bar(jk)` is l, what is the length of `bar(j'k')`? a. m × n × l b. (m + n) × l c. m × l d. n × l

Length of Bar JK=l

Bar (JK) is dilated by a scale factor of n, having origin as the center of dilation.

New line segment formed named  bar (J'K').

As given slope of bar(JK) =m

When we dilate a line segment with respect to origin , having origin as the center of dilation, there is no effect of slope on Dilation.

Length of bar (J'K')= (Length of bar JK)×(Scale factor)

                             = l×n Or n×l

Option (D) is correct.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for