Question

The first term of a gp is 2 and the sum to infinity is 6. find the common ratio

Answer 1

Answer:

Step-by-step explanation:

Formula for sum to infinity term in a GP

S = a / (1-r)

And given here that a = 2

6 = 2 / (1-r)

6 x (1-r) = 2

(1-r) = 2 / 6

(1-r) = 1 / 3

-r = (1 / 3) - 1

- r = - 2 / 3

r = 2 / 3

Answer 2

Given:

The first term of a GP is 2 and the sum to infinity is 6.

To find:

The common ratio.

Solution:

The common ratio is 2/3.

To answer this question, we will follow the following steps:

As we know that the sum of terms of an infinite GP is given by using the formula:

$\frac{a}{1 - r}$

Where a = first term and r = common ratio

Now,

as given in the question,

we have,

The first term of a GP = 2

The sum to infinite GP = 6

So,

using the formula, we get

$\frac{2}{1 - r} = 6$

On solving the above, we get

$2 = 6 - 6r$

$6r = 4$

$r = \frac{2}{3}$

Hence, the common ratio of the given GP is 2/3.