Q. 1. Determine k so that k + 2, 4k - 6 and 3k - 2 are three consecutive terms of an AP.
Q. 2. If mth term of A.P. is , and nth term is , show that the mnth terms is 1.
Q. 3. The first, second and the last terms of an AP are p, q and 2p respectively. Show that its sum is 
Q. 4. A circle is completely divided into n sectors in such a way that the angles of the sectors are in arithmetic progression. If the smallest-of these angles is 8° and the largest 72°, calculate n and the angle in the fourth sector.
Q. 5. Which term of AP: 3, 10, 17 ... will be 84 more than its 13th term?
Q. 6. If 9th term of an AP is zero, prove that 29th term is double the 19th term.
Q. 7. Find a, b such that 27, a, b - 6 are in A.P.
Q. 8. For what value of n, the nth terms of the sequences 3, 10, 17,... and 63, 65, 67,... are equal.
Q. 9. If m times the mth term of an AP is equal to n times its nth term show that the (m + n)th term of the AP is zero.
Q. 10. A person buys National Savings Certificates of value exceeding the last year's purchase by Rs.500. After 10 years he finds the total face value of certificates purchased by him is Rs. 27,500. Find the value of certificates purchased by him in the first year.
Q. 11. In a children's potato race, n potatoes are placed, each, one meter apart in a straight line. A competitor starts from a point in this line which is 5 meters from the nearest potato. Find the expression for the total distance run in collecting all the potatoes bringing one at a time to the starting point. Also, calculate the value of n if the total distance run is 162 meters.
Q. 12. A person borrows Rs.4500 and promises to pay back (without any interest) in 30 instalments each of value Rs. 10 more than the last (preceding one). Find the first and the last instalments.
Q. 13.Find the sum of all integers between 50 and 500 which are divisible by 7.
Q. 14. Find the common difference of an A.P. whose first term is 1 and the sum of the first four terms is one-third the sum of the next four terms.
Q. 15. Each year a tree grows 5 cm. less than it did in the preceding Year. If it grew 1m. in the first year, in how many years will it have ceased growing?
