Question

write the condition under which three numbers a,b,c may be in A.p and G.p both

Answer 1

let t1=a,t2=b,t3=c
Then A.P= t2-t1 = t3-t2
= b-a = c-b
Then G.P= t2/t1=t3/t2
=b/a=c/b

Answer 2

Answer:

In A.P, $2b=a+c$

In G.P, $b^2=ac$

Step-by-step explanation:

Given 3 numbers a, b , c

we have to write the condition under which three numbers a,b,c may be in A.P and G.P both.

In A.P, the common difference remains same

i.e $b-a=c-b$

⇒ $2b=a+c$

In G.P, the common ratio remains same

i.e $\frac{b}{a}=\frac{c}{b}$

$b^2=ac$

These are the condition for both A.P and G.P