Question

1) If a = 1, r = 2, find S, for the G.P. ​

Answer 1

Answer:

Sn for the given G.P = (2^n)-1 ans

Answer 2

Answer:

The sum of n terms of a GP with the first term $a=1$ and the common ratio $r=2$ is $S_{n} ={2^{n}-1 }$

Step-by-step explanation:

• For a sequence in which each succeeding term is generated from its preceding term by multiplying it with a constant number known as the common ratio such sequences are called

        GEOMETRIC PROGRESSION(GP)

• for example, suppose that $a$ is the first term of a geometric progression with a common ratio $r$ then the sequence is

                         $a,ar,ar^{2},ar^{3},$  etc

• we can calculate the common ratio by taking the ratio of the succeeding number to the preceding number

        ⇒ the common ratio of the above sequence $ar/a=r$

• The sum of n terms of a geometric progression is

                       $S_{n} =a\frac{r^{n}-1 }{r-1}$ , $r$≠$1$

from the question,

The first term of GP is $a=1$

the common ratio of GP is $r=2$

substitute these values to get the sum

⇒$S_{n} =\frac{2^{n}-1 }{2-1}\ ={2^{n}-1 }$