Advertisements
Advertisements
Question
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.
Advertisements
Solution
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).
RELATED QUESTIONS
In an A.P., if pth term is 1/q and qth term is 1/p, prove that the sum of first pq terms is 1/2 (pq + 1) where `p != q`
If the sum of n terms of an A.P. is (pn + qn2), where p and q are constants, find the common difference.
The ratio of the sums of m and n terms of an A.P. is m2: n2. Show that the ratio of mth and nthterm is (2m – 1): (2n – 1)
if `(a^n + b^n)/(a^(n-1) + b^(n-1))` is the A.M. between a and b, then find the value of n.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
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.
If the nth term an of a sequence is given by an = n2 − n + 1, write down its first five terms.
Let < an > be a sequence. Write the first five term in the following:
a1 = 1, an = an − 1 + 2, n ≥ 2
Is 68 a term of the A.P. 7, 10, 13, ...?
Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely imaginary?
How many terms are there in the A.P. 7, 10, 13, ... 43 ?
Find the 12th term from the following arithmetic progression:
3, 5, 7, 9, ... 201
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.
Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.
Find the sum of the following arithmetic progression :
50, 46, 42, ... to 10 terms
Find the sum of the following arithmetic progression :
\[\frac{x - y}{x + y}, \frac{3x - 2y}{x + y}, \frac{5x - 3y}{x + y}\], ... to n terms.
Find the sum of all odd numbers between 100 and 200.
The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.
The number of terms of an A.P. is even; the sum of odd terms is 24, of the even terms is 30, and the last term exceeds the first by \[10 \frac{1}{2}\] , find the number of terms and the series.
If Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.
A man saved Rs 16500 in ten years. In each year after the first he saved Rs 100 more than he did in the receding year. How much did he save in the first year?
A manufacturer of radio sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the product increases uniformly by a fixed number every year, find (i) the production in the first year (ii) the total product in 7 years and (iii) the product in the 10th year.
A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much the tractor cost him?
A man starts repaying a loan as first instalment of Rs 100 = 00. If he increases the instalments by Rs 5 every month, what amount he will pay in the 30th instalment?
A carpenter was hired to build 192 window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?
If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be
If the sum of n terms of an A.P. be 3 n2 − n and its common difference is 6, then its first term is
The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
The first three of four given numbers are in G.P. and their last three are in A.P. with common difference 6. If first and fourth numbers are equal, then the first number is
The first term of an A.P. is a, the second term is b and the last term is c. Show that the sum of the A.P. is `((b + c - 2a)(c + a))/(2(b - a))`.
If the sum of m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, then prove that `(m + n) (1/m - 1/p) = (m + p) (1/m - 1/n)`
A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. What is his total earnings during the first year?
The sum of terms equidistant from the beginning and end in an A.P. is equal to ______.
If 100 times the 100th term of an A.P. with non zero common difference equals the 50 times its 50th term, then the 150th term of this A.P. is ______.
The internal angles of a convex polygon are in A.P. The smallest angle is 120° and the common difference is 5°. The number to sides of the polygon is ______.
