18. The difference between any two consecutive interior angles of a polygon is . If the smallest angle is , find the number of the sides of the polygon.
17. A man starts repaying a loan as first instalment of Rs. 100. If he increases the instalment by Rs 5 every month, what amount he will pay in the 30th instalment?
16. Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A. P. and the ratio of and numbers is 5 : 9. Find the value of m.
15. If is the A.M. between a and b, then find the value of n.
14. Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
13. If the sum of n terms of an A.P. is and its term is 164, find the value of m.
12. The ratio of the sums of m and n terms of an A.P. is . Show that the ratio of mth and nth term is .
11. Sum of the first p, q and r terms of an A.P. are a, b and c, respectively. Prove that
10. If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.
9. The sums of n terms of two arithmetic progressions are in the ratio . Find the ratio of their 18th terms.
8. If the sum of n terms of an A.P. is , where p and q are constants, find the common difference
7. Find the sum to n terms of the A.P., whose term is 5k + 1.
6. If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term.
5. 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
4. How many terms of the A.P. are needed to give the sum –25?
3. In an A.P., the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is –112.
2. Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
1. Find the sum of odd integers from 1 to 2001.