If a constant is multiplied to each term of an A.P., the resulting sequence will also be an A.P.

  If a constant is divided from each term of an A.P., the resulting sequence will also be an A.P.

This is written in the study material but in these two cases the common difference is not constant then how these are A.P. PLZ. ANS. FAST...

1) 

If a constant is multiplied to each term of an A.P., the resulting sequence will also be an A.P.

Consider an a.p.: 2, 4, 6, 8, 10, 12

Now, each term in the above a.p. is multiplied by a constant number (say) 3, then the new series is:

2 × 3, 4 × 3, 6 × 3, 8 × 3, 10 × 3, 12 × 3

or 6, 12, 18, 24, 30, 36

Here, the common difference in each term = 6 as:

12 - 6 = 6,

18-12 = 6,

24 - 18 = 6 and so on.

Hence, the given sequence in a.p will remain in a.p if each term is multiplied by any constant.

2)

If a constant is divided from each term of an A.P., the resulting sequence will also be an A.P. 

Consider an a.p.: 15, 30, 45, 60

Now, each term in the above a.p. is divided by a constant number (say) 5, then the new series is:

or 5, 10, 15, 20

Here, the common difference in each term = 5 as:

10 - 5 = 5,

15 - 10 = 5,

20 - 15 = 5 

Hence, the given sequence in a.p will remain in a.p if each term is divided by any constant.

Hope you get it!!

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