# progressions

hiiiiii friends.... i have 1 sum... as i got the answer 3 bt the actual answeris 8 .
as the question follows.....
q: the angles of a polygon are in arithmetic progression .if the smallest angle is 100 degrees and the common difference is 10 degrees,then how many sides does the polygon have?
as i had done in the following way....
in A.P sum on n terms is n/2[2a+(n-1)d] as the first term is the least term a=100 d=10
as in polygon .....sum of the angles =360 as i substituted i got n=3....
is it not the correct way?

## Replies

• Sarathkumar Chandrasekaran
Hi. I also tried but got an wrong answer.As you had said 100 os the smallest angle , i got an answer of 27 sides.
Better fellow CEans knows about it.
• simplycoder
satty lavanya
hiiiiii friends.... i have 1 sum... as i got the answer 3 bt the actual answeris 8 .
as the question follows.....
q: the angles of a polygon are in arithmetic progression .if the smallest angle is 100 degrees and the common difference is 10 degrees,then how many sides does the polygon have?
as i had done in the following way....
in A.P sum on n terms is n/2[2a+(n-1)d] as the first term is the least term a=100 d=10
as in polygon .....sum of the angles =360 as i substituted i got n=3....
is it not the correct way?

According to the question you have provided, it seems that you have considered only the internal angles of the polygon.

Any external angle e= 180-i where i is the corresponding internal angle.

If the internal angles of polygon are in AP then external too would be in AP.(I would leave this to you to verify)

Now when I consider the external angles of the polygon, then
the maximum external angle e would be the corresponding minimum internal angle i,
in our case, it would be against 100 degs.

hence a=180-100=80degs.

Since we are approaching from maximum term, the common difference now would be -10 degs.

Sum of all the internal angles of a polygon = Sum of all the external angles of a polygon, on a 2d rectangular surface=360 degs.

(n/2)(2a+(n-1)d)=360

n(2*(80)+(n-1)*(-10))=720

160n+(n^2-n)*(-10)=720
160n+(-10n^2+10n)=720
-10n^2+170n=720
10n^2-170n+720=0

After Calculating the roots,
n=9 or 8.

When n=9,
Internal angles would vary from minimum internal angle 100 degs to 100+(9-1)*10
=100+80 =180.

This is not possible in a polygon which is defined above.

When n=8, the Internal angles would vary from 100 to 100+(8-1)*10
=100+70=170.

This is acceptable, hence n=8.
• satty lavanya
hi friends .here is the question...
q: a ball is dropped from a height of 144m and it rebounds to two.thirds of the height from which it falls.if it continues to fall and rebound this way,how far will it travel totally before coming to rest?
friends, as the aptitude is useful for every competitive exams. i feel so bad that i m unable to do these sums in less time.... i m unable to catch the logic behind this?
• simplycoder
satty lavanya
hi friends .here is the question...
q: a ball is dropped from a height of 144m and it rebounds to two.thirds of the height from which it falls.if it continues to fall and rebound this way,how far will it travel totally before coming to rest?
friends, as the aptitude is useful for every competitive exams. i feel so bad that i m unable to do these sums in less time.... i m unable to catch the logic behind this?

Once we know what efforts you have put, we can guide you better.
• rahul69
satty lavanya
hiiiiii friends.... i have 1 sum... as i got the answer 3 bt the actual answeris 8 .
as the question follows.....
q: the angles of a polygon are in arithmetic progression .if the smallest angle is 100 degrees and the common difference is 10 degrees,then how many sides does the polygon have?
as i had done in the following way....
in A.P sum on n terms is n/2[2a+(n-1)d] as the first term is the least term a=100 d=10
as in polygon .....sum of the angles =360 as i substituted i got n=3....
is it not the correct way?
Alternate solution:
As the maximum angle of the polygon will be lesser than 180 deg (straight line), so the maximum angle would be 170 deg (as a=100,d=10 ,angles would be similar to 110,120... etc)
Since angles are in AP so,
last term (Maximum angle) = a + (n-1)*d = 170
=> 100 + (n-1)*10 = 170
=> (n-1)*10 = 70
=> n-1 =7
=> n=8
• rahul69
satty lavanya
hi friends .here is the question...
q: a ball is dropped from a height of 144m and it rebounds to two.thirds of the height from which it falls.if it continues to fall and rebound this way,how far will it travel totally before coming to rest?
friends, as the aptitude is useful for every competitive exams. i feel so bad that i m unable to do these sums in less time.... i m unable to catch the logic behind this?
Hint:
Use sum of infinite terms of a GP, try it and share if u face any problems ๐
• Saandeep Sreerambatla
satty lavanya
hiiiiii friends.... i have 1 sum... as i got the answer 3 bt the actual answeris 8 .
as the question follows.....
q: the angles of a polygon are in arithmetic progression .if the smallest angle is 100 degrees and the common difference is 10 degrees,then how many sides does the polygon have?
as i had done in the following way....
in A.P sum on n terms is n/2[2a+(n-1)d] as the first term is the least term a=100 d=10
as in polygon .....sum of the angles =360 as i substituted i got n=3....
is it not the correct way?

I guess you have to consider this, the sum of internal angles of polygon is NOT 360.

If a polygon has n sides then the sum of internal angles is (n-2) * 180.

If you equate the two equations you will get the answer.
• Saandeep Sreerambatla
When I solved this , I got n values as 8 and 9.

So what all the options you had? and I want to know from others if I got two answers, what is the solution here? I have done progressions about 9 years ago!! Please throw some light here.
• akshayyedke123
rahul69
Hint:
Use sum of infinite terms of a GP, try it and share if u face any problems ๐
s=(a)/(1-r)
=144/(1-(2/3))
=432m

but answer in solution is 720m
• akshayyedke123
akshayyedke123
s=(a)/(1-r)
=144/(1-(2/3))
=432m

got it hehe ๐ its 720m.....
• Ramani Aswath
satty lavanya
hiiiiii friends.... i have 1 sum... as i got the answer 3 bt the actual answeris 8 .
as the question follows.....
q: the angles of a polygon are in arithmetic progression .if the smallest angle is 100 degrees and the common difference is 10 degrees,then how many sides does the polygon have?
as i had done in the following way....
in A.P sum on n terms is n/2[2a+(n-1)d] as the first term is the least term a=100 d=10
as in polygon .....sum of the angles =360 as i substituted i got n=3....
is it not the correct way?
Why such complications? The largest internal angle has to be 170 degrees, because 180 degrees makes it a straight line. From 100 to 170 both inclusive there have to be eight angles in AP with 10 degree difference. Hence eight is the answer.
• rahul69
akshayyedke123
s=(a)/(1-r)
=144/(1-(2/3))
=432m

but answer in solution is 720m
See, this 432 is just ball going down, u will also have to consider ball bouncing upward again, so we simply double it
so it becomes 432*2=864
but this 864 also includes upward bounce first time (which did not happen), so we need to subtract the first upward ie 144
so value becomes 864-144= 720.๐
• Amit Rajeshwarkar
satty lavanya
hiiiiii friends.... i have 1 sum... as i got the answer 3 bt the actual answeris 8 .
as the question follows.....
q: the angles of a polygon are in arithmetic progression .if the smallest angle is 100 degrees and the common difference is 10 degrees,then how many sides does the polygon have?
as i had done in the following way....
in A.P sum on n terms is n/2[2a+(n-1)d] as the first term is the least term a=100 d=10
as in polygon .....sum of the angles =360 as i substituted i got n=3....
is it not the correct way?

Easier way : a=100 d=10

so interior angles = 100,110,120....
so exterior angles = 80,70,60,50,..... (180 - interior angles)
But Sum of exterior angles=360
.'. 80+70+60+50+40+30+20+10=360
.'. 8 angles form 8 sides and so n=8
• rajat98064
sum of interior angles of a polygon=(n-2)*180ยฐ
where n=no. of angles =no. of sides
• Ramani Aswath
The internal angle has to be less than 180. The arithmetic progression from 100 to 170 has eight terms. The polygon has eight internal angles and so eight sides. The problem is essentially how many terms are in the progression from 100 to 170 with a common difference 10. The polygon is only a diversion.
• rajat98064
,
rahul69
Hint:
Use sum of infinite terms of a GP, try it and share if u face any problems ๐
Firstly ball travels 144m..then it forms a infinite GP...with the 1st term a=192
(i.e.2*144*2/3) & r=2/3
Total distance traveled =144+192รท(1-2/3)
=720
• Shashank Moghe
satty lavanya
hiiiiii friends.... i have 1 sum... as i got the answer 3 bt the actual answeris 8 .
as the question follows.....
q: the angles of a polygon are in arithmetic progression .if the smallest angle is 100 degrees and the common difference is 10 degrees,then how many sides does the polygon have?
as i had done in the following way....
in A.P sum on n terms is n/2[2a+(n-1)d] as the first term is the least term a=100 d=10
as in polygon .....sum of the angles =360 as i substituted i got n=3....
is it not the correct way?
Sum of the angles = 360? Where did you get that?

Sum of the internal angles of a polygon = 180*(n-2) // n is the no of sides

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