Question

if the three terms of an AP are b,c,2b then find the ratio of band c​

Answer 1

Consider if a, b & c are in AP, then

b = (a + c)/2.

Similarly it is given that b, c & 2b are in AP, then

c = (b + 2b)/2

c = 3b/2

2/3 = b/c

Therefore b:c = 2:3 ——> Answer

Answer 2

Answer:

b : c = 2 : 3

Solution:

The given AP is

b, c, 2b, ...

By condition for an Arithmetic Progression, we write

second term - first term = third term - second term

i.e., c - b = 2b - c

or, 2b + b = c + c

or, 3b = 2c

or, b / c = 2 / 3

or, b : c = 2 : 3

Therefore the required ratio is

b : c = 2 : 3

More on Arithmetic Progressions:

A sequence of numbers or terms

a, a + d, a + 2d, ..., a + rd, ...