Question

if the first three terms of an ap are b, c and 2b then find the ratio of b and C​

Answer 1

Answer:   2:3

Step-by-step explanation:

We know that, If the first three terms of an AP are p,q,r then

$2q=p+r$

According to question we have that b,c,2b are in AP

$\text{That means }2c=b+2b\\\\\Rightarrow\ 2c=3b$

$\Rightarrow\ \dfrac{b}{c} =\dfrac{2}{3}$

Therefore, the ratio of b and c is 2:3                    

Answer 2

The ratio of b and C is "2 : 3".

Step-by-step explanation:

The first three terms of an A.P. are:

b, c and 2b.

Here, first term = b,  second term = c and third term = 2b

∴ Common difference (d) = Second term - First term = third term - second term

∴ $c-b=2b-c$

⇒$c+c=2b+b$

⇒$3b=2c$

⇒ $\dfrac{b}{c} =\dfrac{2}{3}$

Hence,  the ratio of b and C is 2 : 3.