Question

How many terms of the G.P.1,4,16,... must be taken to have their sum equal to 341

Answer 1

hope this helps you.

Answer 2

The number of terms is 5.

Step-by-step explanation:

The given G.P. are:

1, 4, 16, ......

Given, $S_{n} =341$

to find, the number of terms = ?

Here, first term (a) = 1, common ratio (r) $=\dfrac{4}{1}=4$

We know that,

The nth term of G.P.

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

⇒ $\dfrac{1(4^{n} -1)}{4-1}=341$

⇒ $4^{n} -1$=341 × 3 = 1023

⇒ $4^{n}$ =1023 + 1 = 1024

⇒ $4^{n}=4^{5}$

⇒ n = 5

Hence, the number of terms is 5.