Question

if a,b and c are in A.P. show that: (i)4a,4b and 4c are in A.P. (ii) a+4, b+4 and c+4 are in A.P.

Answer 1

If a, b, c are in AP,

b - a = c - b

(i) 4(b - a) = 4(c - b)

   4b - 4a = 4c - 4b

   hence, 4a, 4b, 4c are also in AP

(ii) b - a + 4 - 4 = c - b + 4 - 4

    b + 4 - a - 4 = c + 4 - b - 4

    (b + 4) - (a + 4) = (c + 4) - (b + 4)

    hence, a + 4, b + 4, c + 4 are also in AP

Answer 2

Answer:

a,b,c are in a. p.

Step-by-step explanation:

4b=4a+4c/2

b=4(a+c)/2*4

b= a+c/2

b+4=a+4+c+4/2

b=a+c+8/2-4

b=a+c+8/2-8

b=a+c/2