The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.
The angles of the polygon will form an A.P. with common difference d as 5° and first term a as 120°.
It is known that the sum of all angles of a polygon with n sides is 180° (n – 2).
So
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
Find the sum of all numbers between 200 and 400 which are divisible by 7.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
Find the sum to n terms in the geometric progression x3, x5, x7 ... (if x ≠ ±1)
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3 (S2– S1)
The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.
A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.
Find the sum to n terms of the series whose nth term is given by n (n + 1) (n + 4).
For what values of x, the numbers are in G.P?
They say that the difference between ANY two consecutive angles. So it could be the last and the first one as well but then like Lalit Mohan said the difference is more than 5°. Could you please explain?
Here difference between 16 and 9 is seven. So rejected the value of n=16. So number of sides of polygon is 9.
Here first and last angles are also consecutive, but difference is more than 5.