Mathematics : Arithmetic Progressions

In which of the following situations, does the list of numbers involved make an arithmetic progression and why ?

(i) The height (in cm) of some students of a school standing in a queue in morning assembly are 147, 148, 149........,157.

(ii) The cash prizes (in Rs.) given by a institute to the papers of class X and XII are respectively, 500, 700, 900, ........ 1700.

(iii) The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.

(iv) The cost of painting the wall of a building, when it costs Rs. 50 for the first metre and rises by Rs. 20 for subsequent metre.

(v) The individual academic fee of the institute when it charge Rs. 500 for the first month and Rs. 100 for each subsequent month.

(i) a = 10, d = 10.
(ii) a = –1, d = 1/2
(iii) a = –1.25, d = 0.25.
(iv) a = p, d = –3q. 
(v) a = b, d = 2c. 

Find the next term of the A. P.
Which term of the A.P. 21, 18, 15.....is zero?

Which term of the A .P. 14, 11, 8..... is - 1? 

 (i) For what value of p, are 2p – 1,7 and 3p, three consecutive terms of an A . P. ?

(ii) For what value of p are 2p + 1, 13, 5p –3, three consecutive terms of an A . P. ? 

Find the 10th term from the end of the following A .P. :
(i) 1. 6, 11, 16............201
(ii) 3, 6, 9, 12........... 102