Question

Sum of the series 1 3 9 27 is 364 the number of terms is

Answer 1

Step-by-step explanation:

1,3,(3*3),(3*3*3),....is in GEOMETRIC PROGRESSION

common ratio is "r=3"

first term is a=1

Answer 2

Answer:

The number of terms would be 6.

Step-by-step explanation:

Given sequence,

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

Since,

$\frac{3}{1}=\frac{9}{3}=\frac{27}{9}.....=3$

Thus, it is geometric sequence,

Having first term, a = 1,

Common ratio, r = 3 ( > 1 )

Let n be the number of terms in the sequence,

Then the sum of the sequence,

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

$=\frac{1(3^n-1)}{3-1}$

$=\frac{3^n-1}{2}$

According to the question,

$S_{n}=364$

$\implies \frac{3^n-1}{2}=364$

$3^n-1=728$

$3^n = 729$

$3^n = 3^6$

$\implies n = 6$

Hence, the number of terms would be 6.