Question

if a, b, c are in arithmetic progression show that 4a, 4b and 4c are in arithmetic progression

Answer 1

since a , b and c are in ap therefore it's difference should be equal that is b-a=c-b=d , d for difference in 4a ,4b and 4c ... d= 4b-4a that is 4(b-a) and similarly with 4c and 4b ....d =4(c-b)....there for if we equate all d then 4(b-a)=4(c-a) that is b-a and c- b hence proved