Question

Find the sum of the following infinite G. P. 1/3, -2/9, 4/27,-8/81 ___

Answer 1

Explanation:

I'm following infinite G.P=>

a = 1/3

r = -2/3

Formula for infinite terms are =>

$\frac{a}{1 - r} \\ \frac{ \frac{1}{3} }{1 - \frac{ - 2}{3} } \\ \frac{1}{5} \\ \\ \\ hope \: it \: helps \: uh.........$

Answer 2

Given:

Infinite G.P.: 1/3, -2/9, 4/27,-8/81, so on

To find:

The sum of the infinite G.P.

Solution:

The sum of the infinite G.P. is 0.2.

We can find the sum by following the given steps-

We know that a geometric progression has a common ratio which is obtained by dividing any two consecutive terms.

The first term of the G.P., a=1/3

The second term of the G.P= -2/9

The common ratio, r=second term/first term

r= (-2/9)/(1/3)

r= (-2/9)×(3/1)

r= -2/9×3

r= -2/3

We know that the sum of an infinite G.P.=a/(1-r)

On putting the values, we get

Sum=(1/3)/(1-(-2/3))

=(1/3)/(1+2/3)

=(1/3)/(5/3)

=1/3×3/5

=1/5

=0.2

Therefore, the sum of the infinite G.P. is 0.2.