How Many Terms of the Series 2 + 6 + 18 + ... Must Be Taken to Make the Sum Equal to 728? - Mathematics

How many terms of the series 2 + 6 + 18 + ... must be taken to make the sum equal to 728?

Solution

Here,a = 2
Common ratio, r = 3
Sum of n terms, Sn = 728

$S_n = 2\left( \frac{3^n - 1}{3 - 1} \right)$

$\Rightarrow 728 = 2\left( \frac{3^n - 1}{2} \right)$

$\Rightarrow 728 = 3^n - 1$

$\Rightarrow 3^n = 729$

$\Rightarrow 3^n = 3^6$

$\therefore n = 6$

Is there an error in this question or solution?

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 20 Geometric Progression
Exercise 20.3 | Q 6 | Page 28