Question

How can we assume that four numbers in AP are of the form (a-3d),(a-d)(a+d)and (a-3d) ?
How to represent 5,6,7... in AP?

Answer 1

The following ways are generally used for the selection of terms in an arithmetic progression.
(i) If the sum of three terms in Arithmetic Progression be given, assume the numbers as a - d, a and a + d. Here common difference is d.
(ii) If the sum of four terms in Arithmetic Progression be given, assume the numbers as a - 3d, a - d, a + d and a + 3d.
(iii) If the sum of five terms in Arithmetic Progression be given, assume the numbers as a - 2d, a - d, a, a + d and a + 2d. Here common difference is 2d.
(iv) If the sum of six terms in Arithmetic Progression be given, assume the numbers as a - 5d, a - 3d, a - d, a + d, a + 3d and a + 5d. Here common difference is 2d.
in case of an odd number of terms, the middle term is ‘a’ and the common difference is ‘d’.
Again, in case of an even number of terms the middle terms are a - d, a + d and the common difference is 2d.
5,6,7 are in AP becuase the common difference between successive terms is 1. This can be represented as a-1,a,a+1.