Question

15. Find the following sum 1 + 3 +9+...+2187 in gp
​

Answer 1

Answer:3,9,27,...2187 are in G.P

n  

th

 term of G.P=t  

n

​  

=ar  

n−1

 

a=3,r=  

3

9

​  

=  

9

27

​  

=3

⇒33  

n−1

=2187

⇒3  

1+n−1

=2187

⇒3  

n

=2187

⇒3  

n

=3  

7

 

Since bases are same, we can equate the powers,

∴n=7

please mark as the brainliest

Answer 2

Answer:

Sum of the given numbers in Geometric Progression is 1093

Step-by-step explanation:

• Sum of n terms in Geometric progression , $S_{n} =a\frac{r^{n}-1 }{r-1}$

• nth term is given by, $T_{n}$ = $ar^{n-1}$

where,

a is the first term

r is the common ratio, r≠1 and r > 1

n is the number if terms

According to the question,

nth term , $T_{n}$ = 2187

a= 1

r=3

To find n,

2187 = 1$\times 3^{n}$

$3^{7}$=$3^{n}$

n=7

Sum of the numbers = $1\times\frac{3^{7}-1}{3-1}$

=1093

The sum of the terms is 1093