the first 7 terms of an arithmetic sequence that has a common difference of -2 and whose fifth term is 16.

Comparing how easy this question is vs the other one you posted, my suspicion that you had a typo in your other post stands.

Here:

Since you are using the term "common difference" we can assume that your series is arithmetic.

a + 5d = 24, and d = 4, so

a + 20 = 24

a = 4

your series is

4 + 8 + 12 + 16 + 20 + 24 +

Perpendiculat Line is when both slopes of equation multiplying each others and equal to -1.

For an easier way to understand, a perpendicular line has a negative reciprocal slope. For example if we are given the equation of y = 2x then the equation that is perpendicular to y = 2x would be y = (-1/2)x.

From both equations. We can either arrange in slope-intercepy form or use the slope formula which is m = -A/B when the equation is in Ax+By+C = 0 or Ax+By = C.

To find if these two lines are perpendicular to each others. Use the slope formula of -A/B.

Now recall that it is perpendicular when one of them is negative reciprocal of one another (-5/2 is negative reciprocal of -(-2/5) = 2/5 and 2/5 is negative reciprocal of -5/2).

Or in definition of perpendicular lines, both slopes multiply and must equal to -1.

Thus the equation is true which makes both lines perpendicular to each others.

Answer

Let me know if you have any doubts!