The 17^th term of an AP exceeds its 10^th term by 7. Find the common difference.

Show that a₁, a₂,…..a_n form an AP where is defined as below :

a_n = 9-5n

Also find the sum of the first 15 terms in each case.

In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?

Find the sum of the first 40 positive integers divisible by 6.

Show that a₁, a₂,…..a_n form an AP where is defined as below :

a_n = 3+4n

Also find the sum of the first 15 terms in each case.

If the sum of first n terms of an AP is 4n-n² what is the first (remember the first term is s₁)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd,and the 10th and the nth terms.

A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown in Fig. 5.4. What is the total length of such a spiral made up of thirteen consecutive semicircles? Take π =

[Hint : Length of successive semicircles is l₁ , l₂, l₃, l₄ ,…with centres at A, B, A, B, ….., respectively.]

In a bucket and ball race, a bucket is placed at the starting point, which is 5 m from the first ball, and the other balls are placed 3 m apart in a straight line. There are ten balls in the line.

A competitor starts from the bucket, picks up the nearest ball, runs back with it, drops it in the bucket, runs back to pick up the next ball, runs to the bucket to drop it in, and she continues in the same way until all the balls are in the bucket. What is the total distance the competitor has to run?

[Hint : To pick up the first ball and the second ball, the total distance (in metres) run by a competitor is ]

A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each of the prizes.

Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed and how many logs are in the top row?