Properties of an Arithmetic Progression:
Property I:
For an A.P. with the first term ‘a’ and the common difference ‘d’, if any real number ‘k’ is added to each term, then the new sequence is also an A.P. with the first term ‘a + k’ and the same common difference ‘d’.
Property II:
For an A.P. with the first term ‘a’ and the common difference ‘d’, if each term of an A.P. is multiplied by any real number k, then the new sequence is also an A.P. with the first term ‘ak’ and the common difference ‘dk’.
Note:
1. If each term of an A.P. is multiplied by 0 then the new sequence will be 0, 0, 0, …
2. If each term of an A.P. is added, subtracted multiplied or divided by a certain constant then the new sequence is also an A.P.
