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If a, b, c, are natural numbers in AP an...

If a, b, c, are natural numbers in AP and then the possible number of values of the ordered triplet (a, b, c) is:

A

15

B

14

C

13

D

none of these

Text Solution

Verified by Experts

Since a, b, c are in A.P. Therefore, `2b=a+c`.
Now,
`a+b+c=21implies3b=21impliesb=7" "[:'a+c=2b]`
`:.a+b+c=21impliesa+c=14`
The total number of solution of this equation in the let N of natural numbers is `""^(14-1)C_(2-1)=""^(13)C_(1)=13`
Hence, the possible number of ordered triplets is 13.
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