A circle is the set of all points that are the same distance from one given point. Find an example that contradicts this definition. How would you change the definition to make it more accurate?

ummm what

Step-by-step explanation:

A sphere would contradict this, as its not a circle, but meets those qualifications.  You could eliminate that by saying that the points are coplanar.

, 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