Question

In an infinite G.P, if the first term is 10 and its sum is 30 then the common ratio is​

Answer 1

Answer:

common ratio = 2/3

Step-by-step explanation:

sum of infinite G.P series = a/(1-r)

where a = first term =10

r = common ratio

so, sum S = 10/(1-r)

According to question,

10/(1-r)=30

or, 1-r= 1/3

r= 1-(1/3)

r=2/3

Answer 2

Answer:

Given us a geometric progression (G.P) that has:

• First term, a = 10
• Sum, S = 30

We have to find the common ratio using the given values,

Now,

⇒    S = a / (1 - r)

⇒    30 = 10 / (1 - r)

⇒    30 - 30r = 10

⇒    30r = 20

⇒    r = 2 / 3

Hence, The common ratio, r of the following G.P is 2 / 3.

Some Information:

→  The sum of infinite terms of a Geometric Progression (G.P) having first term a, common ratio r is given by the formula:

                 ⇒     S = a / (1 - r)

Also,  | r | < 1