Question

three non zero number a, b, c are in A. P if and only if ​

Answer 1

Step-by-step explanation:

2b=a+c .(1)

and 2tan−1b=tan−1a+tan−1c

or 1−b22b=1−aca+c Put 2b=a+c

⇒b2=ac by (1) i.e., a, b, c are in G.P.

Also ⇒4b2=4ac

or (a+c)2−4ac=0, by (1)

(a−c)2=0

∴a=c=b, by (1).

Answer 2

Step-by-step explanation:

the common difference between a, b, c should be equal

a1 = a a2 = b a3 = c

d = a2 - a1 = a3 - a2

b - a = c - b

2b = a + c

b = (a + c)/2

if b is equal to (a + c)/2 we can say that a, b, c are in AP

hope you get your answer