Question

if a, b, c are in ap show 4a,4b,4c are in ap

Answer 1

ABC are in ap
Therefore b-a=c-b
Similarly
4b-4a=4c-4b
4(b-a)=4(c-b)
b-a=c-b
Hence proved

Answer 2

Answer: 4a, 4b, 4c are in A.P.

Step-by-step explanation:

Since we have given that

a, b, c, are in A.p.

So, it becomes,

$2b=a+c$

Since 4a,4b,4c

We need to show that it is in A.P.i.e.

$8b=4(a+c)$

$2b=a+c\\\\\text{ Multiplying by 4 on both sides}\\\\4\times 2b=4(a+c)\\\\8b=4a+4c$

Hence, 4a, 4b, 4c are in A.P.