I was reading a chapter arithmetic sequence ,then I came up across a question"the difference between any two consecutive interior angles of a polygon is 5° where smallest angle is 120°.Find the number of the sides of the polygon".But I could be able to solve this question.But my main doubt is which are the polygon which follows arithmetic sequence? Explain with the help of diagram.
Note that the angles are increasing arithmetically by 5°
On
Sum of all angles of a polygon.
$=$$(n-2)180$
Sum of all terms of AP
$=$$\dfrac n2 \big[2a + (n-1)d\big]$
Now you know the first term that is $120$ and common difference $5$.
Note the equation will give two answers $16$ and $9$ but the answer $16$ wont satisfy think why?
Because if a polygon has $16$ sides with the smallest angle $120°$ then one angle will be $180°$ (following the given conditiona of question) thus $180°$ means a straight line.(not an angle to be considered)
Hint: use the formula for the sum of interior angles of a polygon, and the formula for the sum of a finite arithmetic series.