Advertisements
Advertisements
प्रश्न
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
उत्तर
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).
APPEARS IN
संबंधित प्रश्न
Find the sum to n terms of the A.P., whose kth term is 5k + 1.
Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3 (S2– S1)
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
if `a(1/b + 1/c), b(1/c+1/a), c(1/a+1/b)` are in A.P., prove that a, b, c are in A.P.
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 defined by a1 = 3 and, an = 3an − 1 + 2, for all n > 1
Find the first four terms of the sequence.
Let < an > be a sequence. Write the first five term in the following:
a1 = 1, an = an − 1 + 2, n ≥ 2
The Fibonacci sequence is defined by a1 = 1 = a2, an = an − 1 + an − 2 for n > 2
Find `(""^an +1)/(""^an")` for n = 1, 2, 3, 4, 5.
The nth term of a sequence is given by an = 2n2 + n + 1. Show that it is not an A.P.
Which term of the A.P. 84, 80, 76, ... is 0?
The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.
If (m + 1)th term of an A.P. is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.
If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.
Find the 12th term from the following arithmetic progression:
3, 8, 13, ..., 253
Find the 12th term from the following arithmetic progression:
1, 4, 7, 10, ..., 88
The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.
The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.
If < an > is an A.P. such that \[\frac{a_4}{a_7} = \frac{2}{3}, \text { find }\frac{a_6}{a_8}\].
The sum of three numbers in A.P. is 12 and the sum of their cubes is 288. Find the numbers.
Find the sum of the following arithmetic progression :
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
Solve:
25 + 22 + 19 + 16 + ... + x = 115
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?
Find an A.P. in which the sum of any number of terms is always three times the squared number of these terms.
If a, b, c is in A.P., then show that:
b + c − a, c + a − b, a + b − c are in A.P.
If \[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P., prove that:
bc, ca, ab are in A.P.
If a, b, c is in A.P., prove that:
a3 + c3 + 6abc = 8b3.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
The income of a person is Rs 300,000 in the first year and he receives an increase of Rs 10000 to his income per year for the next 19 years. Find the total amount, he received in 20 years.
If m th term of an A.P. is n and nth term is m, then write its pth term.
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
Sum of all two digit numbers which when divided by 4 yield unity as remainder is
If n arithmetic means are inserted between 1 and 31 such that the ratio of the first mean and nth mean is 3 : 29, then the value of n is
If the first, second and last term of an A.P are a, b and 2a respectively, then its sum is
Show that (x2 + xy + y2), (z2 + xz + x2) and (y2 + yz + z2) are consecutive terms of an A.P., if x, y and z are in A.P.
In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term is ______.
The sum of terms equidistant from the beginning and end in an A.P. is equal to ______.
Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.
If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8th terms is ______.
