Question

How many terms of the GP 1,3,9,27......Will make the sum of 1093

Answer 1

Answer:

a(r^n -1)/(r-1)=1093

Step-by-step explanation:

so 1(3^n -1)/3-1 =1093

3^n -1=2186

3^n =2187

n=7

so 7 terms of gp sum makes 1093

Answer 2

The number of terms is 7.

Step-by-step explanation:

The given GP are:

1, 3, 9, 27, ......

Here, first term (a) = 1, common ratio(r) = $\dfrac{3}{1} =3$  (r > 1) and

$S_{n} =1093$

To find, the total number of terms of the given GP = ?

Let n be the number of term.

We know that,

The sum of nth terms of GP

$S_{n} =\dfrac{a(r^{n}-1)}{r-1}$

∴ $\dfrac{1(3^{n}-1)}{3-1} =1093$

⇒ $\dfrac{3^{n}-1}{2} =1093$

⇒ $3^{n}-1=1093\times 2=2186$

⇒ $3^{n}=2186+1=2187$

⇒ $3^{n}=3^{7}$

Comparing both sides, we get

∴ n = 7

Thus, the number of terms is 7.