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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