If a,b,c......in A.P so proved that (b+c),(c+a),(a+b)......in A.P Plz give me solution
vishwajeet , 7 Years ago
Grade 12th pass
Algebra> If a,b,c......in A.P so proved that (b+c)...
2 Answers
prateek
Last Activity: 7 Years ago
FOR A.P. a+c=2b
and 2(a+c)=(b+c) + (a+b)
2(a+c)=b+c+a+b
2(a+c)=a+c+2b
2(a+c)=a+c + a+c {2b=a+c}
2(a+c)=2(a+c)
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Ankur Saha
Last Activity: 7 Years ago
as a,b,c are in A.P. so 2b=a+c..................(i)
If (b+c) , (a+c) , (a+b) will be in A.P. ,,then (b+c) + (a+b)=2(a+c).
Now (b+c) + (a+b)= b+c+a+b =2b+a+c =2b+2b {from(i)}
=4b =2.2b =2(a+c) {from (i)}
SO,,,,,,(b+c) , (a+c) , (a+b) are in A.P. [PROVED]
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