Question

if a b c are in ap then prove that 2a+3, 2b+3, 2c+3 are also in AP

Answer 1

if a b c are in ap then
b-a=c-b
2b=a+c
prove that:2a+3 2b+3 2c+3 are in ap
so. (2b+3)-(2a+3) =(2c+3) -(2b-3)
2(b-a)=2(c-b)
b-a=c-b
2b a+c
hence proved

Answer 2

let d be the common difference
here,
a=a, b=a+2d, c=a+2d
now,
2a+3= 2a+3
2b+3= 2(a+d)+3= 2a+2d+3= 2a+3+2d
2c+3= 2(a+2d)+3= 2a+4d+3= 2a+3+2(2d)
let 2a+3=A and 2d=D
therefore, 2a+3=A
2b+3= A+D
2c+3= A+2D

Therefore it is an AP


plz mark as brainliest if this is correct!!! thank you!