Question

If
the first three terms of an AP are b, c and 2b,
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.

Answer 2

Answer:

b:c = 2:3

Step-by-step explanation:

Since,  the first three elements b, c and 2b are in A.P;

We have to find the ratio of b and c.

For, an AP we know that the common difference of all the terms in the series are the same.

So, we will solve this question by making the common difference of all the terms to be equal..

i.e, the common difference of second term - common difference of first term =common difference of third term - common difference of second term.

i.e , $c - b = 2 \times b -c$

$2 \times c = 3 \times b$

$\frac{b}{c} =\frac  {2}{3}$

∴ b : c = 2 : 3