Question

If the first three term of an A.P. are b,c and 2b ,then find the ratio of b and c​

Answer 1

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, ...

is said to be in Arithmetic Progression, whenever the differences of any two consecutive terms are same. This means that the terms are in the form (a + nd), where a is the first term of the sequence, n is the finite nth term and d is the common difference.